Alright so we will start today with differentiation, when I say differentiation I would also talk about differentiability. Okay so differentiability first of all just like we talked about continuity the last class. So you are not sharing your screen? Okay one second. Can you see the screen now? So you are not sharing your screen? No sir. Yeah now I can. Okay so differentiability is basically testing whether a function has a derivative at a given point or not. So when a function is differentiable and when a function f of x has a derivative at a point So sir I am hearing two voices, I am hearing one of, there is a lag and there is your voice also, I am hearing two voices. Oh yeah last time I also had the same other thing, now is it proper? Okay fine. When a function has a derivative at x equal to a we say that the function f of x is differentiable at x equal to a. Now are you hearing two voices? Now what is the meaning of the fact that a function has a derivative at x equal to a? It means two things. One the function f of x must have a unique tangent at x equal to a and secondly the unique tangent must have a finite slope. Is that fine? Yes sir. Okay now under what circumstances a function may not have a unique tangent at a point x equal to a or it may not have a finite slope tangent at x equal to a. So let us understand when is a function not differentiable at x equal to a that would give us a clear idea as to where the function will be differentiable. Okay so let's take the scenario where f of x or conditions where f of x is not differentiable at x equal to a. The first scenario is when the function is discontinuous at some point when f of x is discontinuous at some point or at that point x equal to a it will not be differentiable at that point also. So last class we had talked about five situations where the function is discontinuous at x equal to a. So any one of those five conditions if it arises the function will be said to be not differentiable at x equal to a. Okay. Okay. Second scenario is when the function has a corner or a cusp or a key at x equal to a. So is that cusp? Yeah see USP cusp. What is corner? What is corner? Are you good? Like this. This is a corner. So at x equal to a this is a corner being formed. Okay cusp is something like this. This is a cusp. Okay this is a cusp. So here it is a corner. So here it is a cusp. And kink is something like this. You have a line and straight away there is a fall like this. So here at x equal to a there is a kink. So I don't get the difference between corner and cusp. Corner is when the two lines meet at the point they form a corner. Okay. So these are lines. These are curves. Oh. Okay. This is a line in a curve. Okay. So at all such points you would find that the function will not have a unique tangent at that point. For example if I talk about mod x function. Yes. When I have talked about mod x function, mod x function graph is a v. So it has clearly a corner at x equal to 0. X equal to 0. This is a function mod x at x equal to 0. Now if I try to make a tangent at 0 by choosing a point to the right of this function. So we all know the definition of mod x function. Mod x function is redefined as x when x is greater than equal to 0 and negative x when x is less than 0. And x is less than 0. Now if I want to find the derivative of the function by choosing a point slightly right to 0 let's say I choose a point 0 plus h. Okay. And I use the first principle that is limit h tending to 0 f of 0 plus h minus f of 0 by h. Let's see what do we get. f of 0 plus h is a positive quantity right. Yes. Now here 0 plus h means you are following the first definition that is x. So it will be 0 plus h means h only. Yeah. Okay. Right by h you get your answer as 1. Okay. So I am getting the slope of the tangent which I am obtaining by choosing a point to the right of 0 as 1. On the other hand if I find the slope of the tangent by choosing a point left to 0 what will I write?  By negative h. Yeah, yeah. f of 0 minus h is a negative quantity so I will follow this definition.  Which will give you negative 1. So basically what I am trying to convince you over here if I try to make a tangent like this this tangent red one will have a slope of 1. On the other hand we have a minus 1. Right, but if I make a green tangent by choosing a point to the left of 0 then this point will have this line will have a slope of negative 1. Right. So this implies I cannot have unique tangent at that point. That means there is no unique tangent at that point. There is no unique tangent at x equal to 0. So the function is non-differentiable at x equal to 0 point. So this criteria is violated. This criteria is violated. Unique tangent criteria is violated. That means violated. And same will happen even when there is a cusp or a kink. Okay. Now even though if the function doesn't have a cusp or a corner or it is continuous at that point it may still be non-differentiable provided the slope of the tangent drawn at that point let's say this is my point x equal to a if this slope becomes infinite then also we say at this point x equal to a the function is not differentiable. Okay. Is that fine? So remember the two conditions when it has a discontinuity it will definitely be not differentiable when it is having a corner it will be not differentiable or when it has an infinite slope of the tangent at that point then also it will not be differentiable. Is that fine? Yes, sir. Now let me just give you a question. Okay, let's take this question. So we have a function which is defined as 4x square minus 4 by x minus 1 when x is not equal to 1 and it is 4 when x is equal to 1. Okay. Which of these statements are true? Which statements are true? Which statements are true? Statement number 1 is limit of f of x as x into 1 exists. Statement 2 f is continuous at x equal to 1 Statement 3 f is differentiable at x equal to 1. Now the options given to you are none of the statements are correct. Option B Option B 1 only is correct. Option C 1 and 2 both are correct. Option D 1 and 3 are correct and option E 1, 2 and 3 all are correct. I think it's none of the above. None of the above. Okay, let's verify this. First is does f of x exist? What is the limit of f of x as x tends to 1 minus 0 by 0 4 Okay, that's fine. So it becomes 4 x minus 1 by x plus 1 by x minus 1 as x is very close to 0 you can just cancel this off. When you put 1 you get 4 into 1 which is 8. Isn't it Isn't it more to be minus x minus 1 in the denominator? Minus x minus 1 is? When you when you redefine the function you will get Why does the function need to be redefined? Is there any mod over here? You don't. Other than generally you generally have to express it in terms of x greater than 1 and x less than 1 and x equal to 1 that makes it easier. Who told you this rule? Sir, I thought. We don't redefine the function. It is already in the redefined shape. I see. Now what is the limit of the function as x tends to 1 plus Same thing I will say. Limit exists. Again limit exists. So this statement is correct? So our statement is correct. But it's not continuous at x equal to 1. It is not continuous because the value at 1 doesn't match with 8. So hence only 1 is correct. Only 1 is correct. Is the idea clear? Now we will take another one. So there is a function which is having a graph like this. The graph is like this. From minus 5 it cuts the x axis goes up. So these all are straight lines. So there are straight lines. There are no curves. Yeah. This is minus 6. This is minus 3. This is minus 1. 0. This is 1. This is 2. This is 5. This is 7. Okay. Yeah. So the curve has been sketched from minus 6 to 7. Okay. Now answer the following question. The question is in the interval 1, 2, 2 f of x is give the equation of f of x. Equation. Yeah. By the way let me give you some values on the y coordinate as well. I have not given you. This is 3. Okay. This is again 3. This is 4. This is 4. Okay. So basically I am trying to find out the equation of the line this line. I am showing it with white color. So you can do point slope form. This line. Of course I can do a point slope form. Yeah. Or you can easily guess from here that it is basically a line which is having a slope of negative 1. Correct. Yeah. Passing through. Origin, correct? Yeah. Or is it passing through origin? This line, this small part is not the whole line is passing through origin. Yeah it is. No, this point, this point over here you can just use your 2 point form. This point here is 1, 3. This point here is 2, 4. Okay. So tell me an equation of a line passing through 1, 3 and 2, 4. You mean to y minus y1 equal to y2 minus y1 upon x2 minus x1 into x minus x1. Right. Y minus y1 is equal to y2 minus y1 by x2 minus x1 times x minus x1. Correct. So this is going to be 1 itself. So this will be y minus 3 is equal to x minus 1. So x minus 1. Just give me a way. Okay. 1, 3 is equal to 2, 3. y2 minus y1 by x2 minus x1. What slope is positive? This is minus 3 actually. So this is minus 3. So it will be Yeah, yeah. So this will be plus, this will be minus 4. Again, this is 2, minus 4. So there is a mistake in writing the points, coordinates over here. So this is 2, minus 4 and 1, minus 4. 2, minus 4 and this is 1, minus 3. Okay. Yeah, yeah. So if you give slope as minus 1. Exactly. So the slope here would be negative 1. So we will have y plus x equal to 2. y plus 3 is negative x minus 1. So y plus 3 is equal to negative x plus 1. So y is equal to negative x minus 4, correct? Yeah, yeah. So plus 4. Sorry, negative x minus 2. This will be negative x minus... Yeah, correct. So this will be the equation of the line connecting that point. Next question is over which of the following interval f dash x equals 0? So f dash x equals 0 in which interval? Or you can say in the intervals. f dash x equal to 0 means the line is parallel to the x axis. Parallel to the x axis. It means minus 3, minus 1 and 2, 5. Alright. So minus 3 to minus 1 and 2 to 5. Okay. Next question is Yes. How many points of discontinuity how many points of discontinuity does f dash x have? How many points of discontinuity does f dash x have? Sir, is it 0? No, no, no. The question is f dash x have. This is the graph of f of x. Read the question properly. How many points of discontinuity? Ask you, plot the graph of f dash x. How would the graph look like? Let's plot the graph of f dash x. So from the interval minus 6 to minus 3 if you look at the function from minus 6 to minus 3 it is a line. What is the slope of that line? Yeah, minus 2 of the 1 2. It is having a rise of 3 and it is having a run of 2, correct? Yeah, 3 by 2. So the answer is 3 by 2. So while I am plotting the graph of this function from minus 6 to let's say minus 3 I would plot it as just 3 by 2 line like this. Yeah. Because I have to plot the slope now. Okay. What will happen from minus 3 to minus 1? It will fall down to the x axis. So it will fall down like this? Yeah. Minus 3 to minus 1. Okay. Yeah. Exactly at this point the function you will see there is a break in the function. It's a break yeah. Correct? I cannot find the derivative at these points. Okay. What about from minus 1 to 0? Minus 1 to 0. It's 3 by It's having a slope of negative 3. Right. It has a slope of negative 3. So it will be like this, correct? Yeah. And this trend continues plus 1 also right? Yes. Because the line here continues to go like this straight till minus 1. So instead of stopping here I have to stop at 1. So till 2 right? No. Till here the line is different. Okay. But here the slope this slope is actually minus 3 but this slope is actually minus of 1. So it will go Yes. It will go at minus 1 position. Okay. Till it reaches 2. So this will be the Again from 2 to 5 2 to 5 again it will be on the x axis. Right. 2 to 5 it will be again on the x axis. 2 to 5 the line will be like this. 5 to 7 Okay. Okay. And from 5 to 7 it will have a slope of I don't know I have not written the points. Okay. I'll show you. Yeah minus 4. So rise is 4, run is 2. So it will have a slope of plus 2, correct? Yes. So plus 2 means it will go up. So let's say this is your point this is your 3 point right? Somewhere over here. This was 3 by 2. So it will be somewhere over here. 3 to 7. Okay. Now tell me how many points of discontinuities are there? 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12. 12 points of discontinuities. Yeah. 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12. 12 points of discontinuities. Yeah. 1, 2, 3, 4, 5, 6, 7, 8. Yeah. Yes sir. Yeah. Yes sir. Okay. So 1 is at top of minus 6. That will be 1 point. Okay. Once again. Here if you have to check the discontinuity, what do you do first? You see the value. Check whether there is a... Remember at corner points what did I tell you? Corner points you said that. The function is starting over here. Okay. So if I take the value of the function at minus 6 and compare it with the limit of the function to the right of minus 6 point. Are they equal? So here it is continuous. It is, no? Yeah. This value is positive. This value is whatever is 3 by 2. The same value is here also. Discontinuity will happen at this position. Discontinuity will happen at this position. Discontinuity will happen at this position. Discontinuity will happen at this position. Discontinuity will happen at this position. Discontinuity will happen at this position and discontinuity will happen at this position. Corner points as of now we cannot tell because you just have to see one important thing which I wanted to tell. If you want to check the differentiability at corner points let's say at minus 6 then we just check whether the derivative at minus 6 plus it should exist and should be finite. That's it. Okay. If you want to check at 7 then derivative at 7 minus must exist and must be finite. Must be finite. Right? Yeah. So here the function is exhibiting 5 points of discontinuity. So those two are taken as 1 point. Okay. Which two are taken as 1 point? I mean the ones which you have circled have taken as 1 point of discontinuity. This itself is a 1 point. X equal to 5 is 1 point only. X equal to 2 is 1 point. X equal to 1 is 1 point. X equal to minus 1 is another point. X equal to minus 3. These are the points, right? Yes. We don't count it as 2 points. There is one X value where it is discontinuous. The next part of the question is from minus 6 to 3 minus 3 what is the value of f dash x? From minus 6 to 3 what is 3 by 2? Minus 6 to minus 3 are 3 by 2. Is that fine? 3 by 2? Absolutely correct? Yeah. Okay. Next question. Which of the following statements about f dash x is false? Statement A. It consists of 6 horizontal segments. It consists of 6 horizontal segments. Okay. Option B. It has 4 jump discontinuities. 4 jump discontinuities. Option C. F dash x is discontinuous. F dash x is discontinuous. In the sets minus 3 minus 1 1, 2 and 5 Option D F dash x ranges from minus 3 to 2 and option E is in the interval minus 1 to 1 F dash x is negative 3. Which of the statement is false? You can refer to this graph also. Sir, I think it's B. It's B? Yeah. Because I have 5 jump discontinuities. Absolutely correct. So this statement is false so B becomes the right option. Is that clear now how to deal with these kind of problems? Yes, sir. Okay. Now, some properties with respect to differentiability. Properties of differentiability. First property is if your f of x function is differentiable at x equal to a then any constant multiplied to the function will also be differentiable at x equal to a. Okay. Second property is if f of x and g of x are differentiable at x equal to a then the sum the difference the product. They will also be differentiable at x equal to a. Okay. Even the ratio is also but provided g of a should not be 0. Sir. Can you put this session on YouTube? Yes, yes. Okay. Okay. Why what happened that makes you conscious. So little so happens. Don't worry. Fine. Yeah. And one of the most important property is if f of x is discontinuous at x equal to a then f of x is definitely not differentiable at x equal to a. Correct. Okay. But if f of x is continuous at x equal to a then it may or may not be differentiable at x equal to a. Are you getting this point? Yes, sir. We will now start talking about differentiation per se. I think in the class we had already talked about differentiation of implicit function differentiation using logarithmic function, correct? Yes. So I will quickly just take few examples and move on because I don't want to waste our time doing the same stuff. Hope you are aware of implicit differentiation. Yeah. Can I give you a problem on that? Okay. So let's take this question. So we have a function we have an equation like this which is an implicit one. Okay. Yes, sir. Find dy by dx. So do you remember the formula which we discussed the other day? Do I? Do you remember the formula that we discussed the other day? Make this as f of x, y equal to zero. Then dy by dx is directly given as minus dou f by dou x divided by dou f by dou y. Yeah. So you can directly use this formula here. So bring this minus one on this side even though it is not required but let's say I bring the minus one. Had there been some other function in x and y you should always bring it to one side. This is what we call as f. Correct? Yeah. So this is negative of partial derivative of this with respect to x. So what is the partial derivative of this with respect to x? It will be 6x. It will be minus 2y. And the rest of the thing will be zero. Yeah. Correct? Yeah. Divided by dou f by dou y. So what is the partial derivative with respect to y? This will be zero. Okay. Yeah. So if I drop the factor of 2 what will I get? Negative. 3x. Negative 3x. Negative y. So I can write it as 3x minus y by x minus 5y. Yeah. Yeah. And this is your implicit differentiation. So this is actually a part of your CBC curriculum as well. That's why I'm not spending a lot of time on this. Okay. So I'll move directly to parametric differentiation. I think this is also something which we had already done in the class. Yeah. So let's take an example on this as well. Let's say I have a question x is e to the power theta cos theta y is e to the power theta sin theta. Find d2y by dx square at theta is equal to pi by 2. d2y use logarithmic function also in this. Is it required? You may use I mean I'm not saying you cannot but is it required here? Because let's say if I have to find dy by dx I can use the formula dy by d theta divided by dx by d theta. Yeah. To differentiate this I don't need log actually because I can directly use product rule. So e to the power theta derivative of sin theta will be cos theta plus again e to the power theta sin theta. Minus. What about the denominator? Divided by e to the power theta sin theta minus e to the power theta cos theta. Correct. Now if you want you can get rid of theta from everywhere so it becomes cos theta plus sin theta by cos theta minus sin theta. Okay.  Excellent. Okay. It's tan of 5 by 4 plus theta. 5 by 4 plus theta. Now having got dy by dx as tan of 5 by 4 plus theta what would be your d2y by dx square term? D2y by dx what? Derivative of dy by dx correct? 6 square theta. What will I write? 6 square theta. 6 square theta or 6 square pi by 4 plus theta. That's it. Theta by d theta by dx Absolutely. Please don't forget here your function is in terms of theta but you are differentiating with respect to x so you have to use the chain rule over it. Yeah. Now so secant square pi by 4 plus theta and d theta by dx would be reciprocal of dx by d theta so reciprocal of this term so that will be 1 by e to the power theta 1 by e to the power theta cos theta minus theta. Now you have to evaluate this when theta is pi by 2. So secant square here if you put pi by 2 you get 3 pi by 4 into 1 by e to the power pi by 2 this will become 0 minus 1 correct? Yeah. Pi by 2. What is secant square 3 pi by 4? 6 square 5 by 4 6 square pi by 4 2 divided by minus e to the power pi by 2 that will become your answer or negative 2 by e to the power pi by 2 or you can say negative 2 e to the power minus 1 is that fine? Yes, sir. Okay. So next concept that I am going to talk about is slightly new to you that is the concept of derivative of inverse of a function. Derivative of inverse of a function. I think we had already discussed the concept of inverse of a function in our function chapter. Yeah. So if f of x is the function its inverse is represented by f of x minus 1. Yeah. Now we also know from the graph that these two functions are actually mirror images of each other about y equal to x. Y equal to x line, yeah. They are mirror images of each other about y equal to x line. Okay. So I will give you a scenario. Let me see how do you analyze that. So let's say I have given you a sketch of a function something like this. Okay. And let's say this point here is 3, 8. Let me call this point as point A. Okay. So point A is 3, 8. Correct. Yeah. Let's say at this point I sketch a tangent. Okay. And I say that the slope of this tangent is 5. Yes. Yes sir. Okay. The function is y equal to f of x. I want to know from you what is f dash 8. Sorry.  Let me write in a proper way. So what did be 5? f inverse dash. So what did be 5? Are you sure? Yeah. Sir, it's wrong. It's over half a minute. Sir, it will be the slope of the line which is reflected about the yx above 1 equal to x line. Okay. First question. How would be the graph of f inverse x? Okay. This is, this line is your y equal to x line. Okay. So it will be inverted about that. Right. Yeah. So if I am not wrong will it look like this or not? Correct. Yes. If this point A is 3, 8 what is the mirror image of this point let's say about the y equal to x line. What will be this point B? Can you tell me that Shreya? Yeah. Y equal to x line. It's 90. If 3, 8 is reflected about y equal to x then what is the coordinate of B point? So B is the reflection of A about y equal to x. Won't it be 8, 3? See x equal to y means x and y are interchanging their positions, isn't it? Whatever is on the x axis will go on the y. Whatever is on the y will go on the x. So basically you can treat this as a mirror which is reflecting the points from y axis to x axis and x axis to y axis. Correct? Yes. Now when I ask you the question find the derivative of f inverse at 8. What did I mean by that? You have to find the slope of the element I want to find the slope of the tangent at this point. Correct? Yes or no? Yes sir. Now how is the slope related? Let me just give you a quick analysis over here. Let's say I want to treat the slope of this as the ratio of these two quantities. Okay? So if dy by dx is your 5 let's say dy by dx is 5 that is rise by run is your 5 Correct? Yes. In this case what will happen? In this case you would realize the same dy will now come over here and the same dx will now come over here. So for this it will be the dx by dy ratio. So if dy by dx is 5 then what will be dx by dy? 1 by 5. Absolutely correct. So the slope here will be 1 by 5. Are you getting this point? Yes sir. This I tried to show you geometrically. Okay? Yeah. Mathematically if I have to explain this then I would use a very important theorem which is this f of f inverse x that's always x. But only if it's 0. And same is true for this. That means it is a function which actually returns the same value as you input to it. Yes sir. Is that fine? These two properties will be very helpful even when we are dealing with questions involving inverse of functions. Is that fine? Yes sir. Now see. Let's say I take the second equation for the previous question itself I was given that f dash 3 was 5 and we wanted and we wanted f inverse dash at 8 and it was given that the curve was passing through 3, 8 wasn't this the information given to us in the previous question? Yes sir. So slope of the function at 3 was given as 5 the value of the function at 3 was given as 8 and we were asked to find out the slope of the tangent drawn to the inverse of the function at 8 point. Yes or no? Yes sir. The expression f inverse f of x is equal to x. Let's differentiate throughout with respect to x. Let's differentiate with respect to x. What do we get? We get f dash of inverse f of x into f dash x is equal to 1. Yes. Just try to recall this. You would be knowing this. If you want to find the derivative of this with respect to x. I told you in the class also it's f dash g of x into g dash x. That's what we call as the chain rule right? Yes sir. This itself is your chain rule. Now here I need f inverse dash at 8. Can I write it like this? Okay. I brought this term to the denominator. Yes. If you want this term to be 8 what should be your x value? Look here. Absolutely. If you want f inverse dash at 8 you have to put x value as 3. 5. 5. So your answer is going to be 1 by 5. Is that correct? Okay. Can you conclude that the inverse of a function will have the reciprocal of the slope? The derivative of the inverse of a function will be inverse of the slope. Is that right? See derivative at which point that is also important right? See here you are finding the slope at 3 to be 5. At 3 the slope is 5 but here the slope at 8 is 1 by 5. Right. It's because 8 is the very point that you get when your x is 3. So basically the curve was passing through 3, 8. So yes if these two reverse that means f dash f dash at 3 would be reciprocal of the inverse dash at 8. This you can say if the curve is passing through 3, 8. Okay. So if you want to generalize you can generalize it like this.  Lies on f of x. Okay. Then I can say that f inverse dash calculated at b will be 1 by f of f dash calculated at a. Are you getting this one? Yes sir. This you can generalize. Okay. Let's take another question based on this. If your function f of x is defined as x2 plus x minus 2 and let g of x be the inverse of f of x. Okay. Evaluate g dash 0. Evaluate g dash 0. Of course yes. Let's say it is a non calculator based question. See here the idea is if you want to find g dash 0 it will be reciprocal of f dash that value of x which will give you the value of this as 0.  Can you guess that the value will actually be 1?  Okay.   So your answer is going to be 4. So this is going to be your answer. Understood how it works? Yes. Let me see if I can give you another one. Okay let's take this question. If f of x is given by 2x cube minus 3x and x is the inverse of f of x then h dash minus 1 will be equal to 2x cube. Good carefully. Yeah. We cannot get 2 answers. So what do you do first? I found the derivative of f of x. It has to be 1 by derivative of f at such a value a where this gives you the value as negative 1. Yeah. So 2a cube minus 3a plus 1 equal to 0 again I can see a equal to 1 is a possible value. Yes sir. f dash 1.  So your answer will be what? 3. 1 upon 3. 1 by 3. Is that fine? Yes sir. Now couple of things that differentiation actually helps us in is first it also helps in evaluating limits in many of the cases by the use of a very important rule called the Lopital rule. Lopital rule. Okay so are you aware of this rule? Yeah. So can we do some questions where we can evaluate the limits by using Lopital rule? To differentiate and then apply the limits that you eliminate the 0 by 0 form. Okay so I will just review it for you. Lopital rule is applied to problems of this nature where the indeterminate form involved is 0 by 0 or infinity by infinity. And how do we evaluate the limits in such cases? We actually differentiate the numerator function and denominator function separately. Put this value a to see if it gives me a finite value. Correct? Yeah. If indeterminacy persists the process is repeated. What process? The process of differentiating the numerator and denominator and putting the value of X equal to it. So that process will repeat. Okay. So I will give you a simple example to understand this. Let's say I want to evaluate limit extending to negative 2 not negative 2 let's say I take infinity X cube minus 4 X square plus 7 divided by 3 minus this. Right? I think the answer for this is already known to you by the fact that it's since the degree of the numerator and denominator is same it's just 1 by minus 2 right? Yes. Let's say I want to solve this by using Lopital. First I would ask myself can I apply Lopital over here that means is it 0 by 0 or infinity by infinity form? Yes. The answer is yes. So what we do is we differentiate the numerator we write 3 X square minus 8 X divided by minus 6 minus 6 X square again it's infinity by infinity so we will continue the process 6 X minus 8 and then again since it is infinity by infinity we will continue the process and ultimately we get the answer as minus 1 by 2. Now here the word applied to is important because unless until it is in these two forms you cannot apply it but nevertheless you can actually use to solve any indeterminate form question for example let's say I want to solve this question limit X to the power 1 by X extending to infinity which indeterminate form is exhibited over here can you tell me? Infinity raised to 0. Absolutely this is infinity raised to the power 0 form I can still use Lopital to solve this question. Let's say I call this as L take log on both the sides the base of E so can I say taking log on this will become 1 by X ln X 1 by X ln X so it is nothing but it is nothing but ln of X by X so do you see now it is of infinity by infinity form so now again you differentiate now we can apply Lopital on this so if you differentiate your numerator what do you get? 1 by X if you differentiate your denominator you get 1 and add in 3t this value is going to be 0 so it is a finite value so I will stop over here so ln of L is 0 so what is your L? again you differentiate L is 1 oh different we will stop over here okay understood? yes sir I will give you one more yeah what is limit of X sin 1 by X as X tends to infinity X tends to infinity X in determinant form why not? because it will be X into sin 0 which is 0 so 0 into infinity is an indeterminate form this is another indeterminate form so can I apply Lopital in this present form of the problem? no sir it doesn't work so first of all what do I do? first of all it can be your product rule hey there is no product rule first of all I have to bring it to 0 by 0 form or infinity by infinity form there is no product rule applied and all in Lopital the differentiation of numerator and denominator separately please remember when you are doing F dash A by G dash A you are not applying any kind of a quotient rule you are differentiating it separately and this you are differentiating it separately but you cannot start the process of differentiation unless until you have brought it to 0 by 0 form or infinity by infinity form so how did you know you have to make it like that? what else option do you have? you could have made X divided by cosec of 1 by X that is fine but cosec will involve a bit of lengthy differentiation process this was the most simplest I could think of so the idea is you have to manipulate with your function and bring it to 0 by 0 or infinity by infinity form even before you start differentiating the numerator and denominator yes sir not tell you what is the derivative of sine of 1 by X with respect to X cos cos 1 by X into 1 by 2 root X 1 by 2 root X minus 1 by 2 root X where root 2 X comes and then denominator will be minus 1 by X correct when I get cancelled so X divided by 8 will be this term and this term gets cancelled and this will actually lead the answer to 1 because this quantity is very very small but close to 0 and cos 0 is going to be 1 okay in reality if I just show you the graph of X sine 1 by X you will understand how it actually works the graph of X sine 1 by X you see a graph like this it comes from 1 comes down over here oscillates very vigorously and again even dies at 1 so this line is actually Y equal to 1 line so Y equal to 1 is asymptotic to this it is helpful to know this graph because it is very widely seen in AP calculus is the idea clear okay so let's take another one evaluate plus H minus 1 by H H tending to 0 which form of indeterminancy is here 10 which 0 by 0 can I apply Lofikar directly on this no I can't why can't I I just said no but I can't hear you my question is we can't can't we apply Lofikar on this because it's 0 by 0 okay so what will be the derivative of the numerator a separate differentiation we have to do so it's 1 by E plus H into yeah 1 by E plus H derivative of E plus H E is constant yeah so it's 1 what's the derivative of minus of 1 0 what's the derivative of H with respect to H 1 so now when you put H as 0 in this it is 1 by E is it a finite answer so this becomes my answer oh right I started using those standard limits no we are applying Lofikar over here don't worry evaluate the limit 1 plus tan 5 by 4 minus x raised to the power of c to x where x is sending to 5 by 4 yeah so you use logs right right so let's say this is L so you first make it as H tending to 0 you take minus 5 by 4 equal to H first want to do that I have taken logs first okay then what do I do next so I can write this as limit extending to 5 by 4 ln of 1 plus tan 5 by 4 minus x divided by cos of 2x right now which form of indeterminancy is here 0 by 0 0 by 0 0 by 0 can I apply Lofikar over here I thought shouldn't equal to H shouldn't you do that because it's not ending to 0 doesn't matter can do that you want to do this x is 5 by 4 plus H and then you make H as 0 you can do it because it doesn't make a difference to your answers so let's say okay let me do that first so this will become H tending to 0 ln of 1 plus this will become minus H so I'll write it down as negative tan yeah negative tan raised to cos divided by this will become cos of 2x so cos of 5 by 2 plus 2H what is that negative sin never mind do it no worries now once it has been reduced to 0 by 0 form can we apply LH rule yes we can 1 upon tell me what is the derivative of ln of 1 minus tan H 1 upon 1 minus tan H into minus x square H what happens what happens to the derivative of minus sin to H it becomes cos minus cos to H the negative gets cancelled into 2 right yeah yeah into 2 yeah yeah sir now when you put H as 0 it becomes 1 minus 0 this will become 1 by 2 so what's your answer half but this is ln of the limit so what is limit itself 2 e to the power e to the power half ln L is half ln is e to the power half yeah yes sir okay now we will quickly talk about the mean value theorems under mean value theorems we are going to study two theorems one is called the rose theorem and other is called the langrange's mean value theorem sometimes this is only referred to as mean value theorem they may not use the word langrange's okay I have seen in your ncrt syllabus also curriculum they avoid using the word langrange's they just refer this as mean value theorem okay so both of these theorems essentially talk of the same thing and let me start with rose theorem rose theorem says if there is a function which is continuous in close interval a to b and it is differentiable in open interval a to b and if f of a is equal to f of b then there exists let me write k over a then there exists at least once c belonging to the open interval a to b where the derivative of the function becomes 0 so this whole theorem is actually known by the name of rose theorem which was given by michael roll in 16th century now what does this theorem actually mean geometrically is something which is very obvious so mr roll meant that if you have a function like this i am just taking a simple example if you have a function which is continuous from a to b let's say this is your a let's say this is your b and let's say it doesn't have any kind of corner cusp that means it is differentiable also in the open interval a to b and f of a and f of b have the same values so let's say this is your f of a and it is same as f of b then it says that there will exist at least one point c where you would realize that the slope of the tangent becomes 0 at this point this is having a slope of 0 so f dash c becomes 0 that means it will become parallel to the x axis which is 0 now why at least one c because you can have a situation like this also let's say this is a okay there are like 3 points yeah so here we can have 3 points one is this point let's say alpha let's say beta let's say gamma where the slope of the tangent will start becoming 0 so it's very obvious thing that he stated okay let me take a question on this demonstrate rho's theorem for the function x sin x on the interval 0 to pi the graph is just showing that it's x equal to 0 without drawing the graph also you can do there is nothing like you have to always draw the graph but you have to use a calculator for this definitely how to solve equations on calculators probably know how to use a calculator for graphs not solving equations no no sir I just try the graphs so please try that out also today because many a times you would need to use your calculator to solve equations which you cannot directly solve now here if I have to demonstrate rho's theorem the first thing that I need to show that f of x which is your x sin x is continuous function in 0 to pi how how it is continuous in 0 to pi it's very simple because you know the property of continuity that if there are two functions if x is continuous x is continuous and the product is also continuous absolutely correct f of x is also differentiable in the open interval 0 to pi 0 to pi and again why is that so because x is differentiable from 0 to pi sin x is differentiable from 0 to pi perfect now is f of 0 equal to f of pi yeah yes because 0 will make it 0 and pi will make sin pi 0 both are same both are equal to 0 now rho's theorem says that the derivative of the function at c will vanish for at least at least one c belonging to the interval 0 to pi that's what it's trying to say so we have to demonstrate that this actually happens this is the step that we need to show right so we need to show this or we need to demonstrate this okay so first of all what is the derivative of the function x it's x cos x plus sin x correct and let's say I am finding at c so that means I am putting x as c so it is c cos c plus sin c correct and if I am putting it 0 I need to know my c first okay now there are various ways to solve it one is in your calculator other is if you see this something like this c is equal to minus just minus tan c correct I am sorry that means I am trying to see where does minus of tan x meet the line y equal to x correct so let me take you to g o g bra y is equal to negative tan x and y is equal to x correct so you would see here that in the interval 0 to 5 this is the point where they meet which point this is the point a a is 2.03 radians it will always give you radians okay yeah so I can say that the value of c over here is going to be 2.03 radians so c here comes out to be 2.03 radians which definitely belong to the interval 0 to pi and hence a rose theorem is verified or demonstrated please don't write rose theorem is proved because rose theorem is already proven you are just verifying it is that clear how it works yes sir okay let me pick up another example in fact in your Aadi Sharma when you open you will find a lot of questions on rose theorem okay so without wasting much time can I go to lang ranges mean value theorem okay so lang ranges mean value theorem which basically a generalization of what rose theorem actually meant okay so lang ranges said that if your function is continuous in or on the closed interval a to b and if your function is differentiable in open interval a to b then there exists at least one c belonging to the open interval a to b where the derivative of the function at c is nothing but the slope of the secant line connecting a and b the slope of the secant line connecting the points a and b let me show you from a graph so lang ranges was very smart person so what he did he actually took the same concept as what rose said okay let's say this is your function which is continuous in the closed interval a to b differentiable in the open interval a to b then he said that there will exist at least one c let's say this is that point c where the slope of the tangent will become same as the slope of the line connecting let's say this point a with b so these two will actually become parallel in fact in this given diagram you can see there would be two such points one would be like this as well yeah three like that so you can have let's say alpha you can have beta whose slope will be parallel to the secant line connecting a and b okay it's like saying that when you are travelling on a car the average speed of your car will match with the instantaneous speed at some value of your time in the journey okay so this is nothing but your average velocity this is nothing but your instantaneous velocity is that fine just one moment I will get a problem on this so we will take a question verify row's theorem for x-a to the power n x-b to the power of n so is this the continuous function let's say I give you the interval from a to b is it continuous is it differentiable yes so what's the derivative of this function true x-a raised to m into nx-b raised to n-1 into d by dx of x-b which is 1 into 1 plus x-a raised to m and x-b okay yes so what is f of b-f of a by b-a can I say it will be 0 only so that means c-a to the power m-1 c-b to the power n-1 m c-b plus n c-a will be equal to 0 yes now assuming that these two assuming that c is not equal to a and c is not equal to b this will be equal to 0 then what I'm trying to say I'm trying to say that c lies between open interval a to b c cannot be a or c cannot be b open interval it cannot take the values at the extreme positions so this becomes m plus n c is equal to m-b plus n-a so c is nothing but m-b plus n-a by m plus n I should have mentioned over here m and n are natural numbers do you see this is actually like a section formula yes so your point c has to be somewhere between a and b hence mean value theorem is very nice do this verify verify mean value theorem for this function on the interval 0 to pi so Tuesday I will be sending you a test of onr yeah everything will be included so is it a continuous function in 0 to pi because it made up of some of two continuous functions right is the differentiable function also because it is made up of some of two differentiable functions so all I need to show that there exists a c which will satisfy this criteria by pi minus f of 0 by pi minus 0 where your c should belong to 0 to pi open interval what will be f dash c cost to x is to cost to x correct cost to x f of pi would be what 0 f of 0 will also be 0 okay so this will be 0 itself so that means cost c plus cost to c is 0 if you use your transformation formula you can say it is to cost 3c by 2 into cost c by 2 is equal to 0 so this implies 3c by 2 could be values like pi by 2 okay 3 pi by 2 pi pi by 2 etc and even c by 2 could be values like pi by 2, 3 pi by 2 pi pi by 2 etc from this top one I can get a value of 3c by 2 let's say equal to pi by 2 then c is equal to pi by 3 rest other values will either be pi or exceed the interval and here the minimum value is pi so we got this value as our one of the values which belongs to the interval 0 to pi which satisfies our main value theorem is it clear how these main value yes sir okay great so I'll give you some questions in general there is a parabola y is equal to x square minus a tex plus 10 okay x value isn't equal to 4 question is find g inverse sorry g dash c where g is the inverse of this function this is first question second question is f of u is sin u and u is x square minus 9 find f o g dash at 3 first one should give you the options for the first question should I give you the options okay minus half minus one sixth one sixth half 11 by 2 okay so g dash of 3 will be 1 by f dash of a where this a is such a value which will actually give you this as 3 correct okay so here a square minus a tex plus 7 is equal to 0 this is factorizable as this yeah so which one will you choose will you choose 1 or 7 you choose 1 because x is less than absolutely correct since x is less than 4 will only choose 1 will not choose 7 correct so my answer will be 1 by f dash 1 right so what is f dash 1 f dash 1 will be dy by dx at 1 that is going to be 2x minus 8 at 1 that is going to be minus 6 so your answer is minus 1 by 6 what did you say minus half okay next one second one 0 okay how do I get this first sign you so basically one second I think I forgot to tell what is your g in this case correct g is actually your u in this case give me one moment this is your g actually so what is f of g so what is the derivative of this minus 9 into what should I do that cos of x cos of x is 9 into 32x correct yeah so what is your answer then cos 0 into 6 which is 0 which is 6 okay yes now the last part of this chapter is something which is very easy this is called estimating a derivative at a point estimating a derivative numerically now you would have learnt about the first principles right when you find the derivative of a function at a what do we do we take the limiting case of f of a plus h minus f of a by h correct okay now there is something called symmetric difference quotient symmetric difference quotient which actually helps us to evaluate f dash a in a better way like this f dash a is given as limit h tending to 0 or you can say it is approximately equal to let me remove this approximately equal to f of a plus h minus f of a minus h by 2h okay indirectly it's nothing but it's an average of it's an average of the progressive derivative expression how do you do that how do you convert how do you make it f of a plus h minus f of a minus h by 2h see what happens when we are finding the derivative at a let's say okay what do we normally do we normally take a point slightly right to the function let's say a plus h correct yeah okay and let's say this point is a comma f of a then we draw a secant line like this yeah correct we find the slope of the secant line as y2 minus y1 by x2 minus x1 correct no yeah now what instead of doing this if I take a point to the left of a let's say a minus h then this point will be a minus h comma f of a minus h correct and if I take the limiting case of this secant line let me show you in white color then what do I write I will write f of a plus h minus f of a minus h that is y2 minus y1 by x2 minus x1 what is x2 minus x1 2h this is what I have written over here okay because many times question comes to evaluate the approximate value of derivative at a given point let me take an example to show you this let's say this is a differentiable function it follows the following values so at 1.0 its value is 8 find f dash 1.5 find f dash 1.5 so what I will do is this value is approximately equal to f of 1.6 minus f of 1.4 divided by 1.6 minus 1.4 so I am using this formula f dash a is approximately f of a plus h minus f of a minus h by a plus h minus a minus h here what is my a 1.5 here what is my h h is 0.1 okay so from this I get so this value can easily evaluate from the table given to you minus 14 by 0.2 that is 8 by 0.2 which is 4.5 okay this is how we get the estimate value of the derivative at a point by using symmetric difference quotient so here we will end up the session right now okay and I will share with you the assignment


or under the hashtag C3T on Twitter. All right, welcome. We wanna show in how in Austria we are addressing the subject of state surveillance. We wanna do this by two lines of argumentation. First of all, the abstract apparent threat that is being portrayed bigger than it actually is to give reason to further surveil and then downplay, on the other hand, the consequences that surveillance has on the regular folks. So we will look at this language that's being used very precisely and to understand how surveillance is being justified. Thank you, Angelika, that is our law person amongst us, our advisor. My name is Thomas Lohninger and we're gonna speak on behalf of EpiCenter Works. We're a company that is maybe mostly known for data saving and that we took to the European High Courts. So if you don't know us that, you might know us from Nat Neutrality with safetyinternet.eu. We pushed for Nat Neutrality in Europe, but thank you very much. There was a round of applause. But continue to Werner Reiter, my other colleague up here with me. All right, I've never spoken in front of this many people. I'm a little bit nervous. Please help me out. There's a round of applause for him as encouragement. That was not the question. The question was, please raise your hands who does not like state surveillance or a state-run Trojan horse. Everybody's raising their hands. Basically, well, there's not a few people. Now I have something for you. We have a video, but we don't have a sound. We'd like to show the video now with sound. We're now listening to a video. Everyone in the parliament who is pushing back against the kind of security package that we're trying to pass are basically attacking the Austrian public to not have security that other countries already have. All right, that is Wolfgang Tsuveta, former Minister of Inner Security, and he basically showed his response to you not wanting to be snooped upon, and you're basically being made out to be the attacker onto safety of a state. The emotional blackmail that is part of this statement is a real bad thing.  Sorry. What is this topic, and those people who know me will know that we've discussed proposed laws for Austria in 2017 of the black-red government. We'll come to the current developments, but at the moment it's not all that sure. So today is what has the second highest office in the state, and he has set it as clearly as no other, and here are the measures that he wanted that caused us to take action here. So he's asking for networked video surveillance. He wants tickets in public transport and he wants cars tracked. So he wants all movement of anyone tracked. The thing that was discussed most was the, the Trojan software, the spy software that they wanted to employ. Since Nodin, we have end-to-end encryption, and they want to break into it, and this is why they want the Trojan. This kind of espionage software has been tried to make legal in 2016. When our Justice Minister wanted to try and make it possible, and we tried to stop it then, and it was taken back before it was even finalized. And in 2017 they tried again. But they always want this kind of surveillance. So our campaign was to stop this whole package of surveillance measures. In the civil society we found many supporters for this. And this campaign covered all of Austria, not just the network, not just Vienna, but all towns. We made a hotline where you could call politicians and convince them that this was a bad idea. Oh, that it goes far beyond anything that is compatible with our base price. And we all also called Mr. Buch at 11 on Thursdays to tell them that this wasn't a bad idea. And we also produced a tool with which you could participate in the public survey and submit your own opinions. So it was proposed, there was a long debate about it. Then there was a long wait until the summer break, and then just before the summer break the original proposals were made even worse. So they wanted to introduce a network censorship, and they wanted to have those filters under the guise of protecting the youth and filtering out pornography. They also wanted to extend mobile catchers and wanted to extend them to cars. And we also had prevented the... the foot tracker for dangerous people. So what we are asking for is protection of private... Not every form of surveillance is automatically contradicting the constitution. And there must be multiple aspects for this to be compatible. And the main aspect is that it needs to be appropriate. And during the whole debate there's never a justification on how it would improve security and the compatibility and the appropriateness is never proven. So we see it as a danger to our freedom and ironically also to our security. So we insist that all of those things together are checked for their compatibility with our basic rights. So we're going to go back further a bit to the very beginning. So what was the starting point for all of this? The sound is not very good, but it's a historic video and I've got to show you. And I have a very personal example. It's a few years old back then.   I hope with subtitles it's fine. You probably also misunderstood what he was saying.  And I mean this is very symptomatic for this kind of debate on security in Austria and probably also for other countries. You try to fight the symptoms with placebos to really speak about the reasons for stuff. And which is when we get to politics of emotions. And now we're going to watch the second part of the video. And the surveillance of the camera and that it's only a security feeling and that gives people the feeling of security. So this is a very essential kind of term that's being used in the debate on security. It's about this subjective security feeling. It used to be a feeling for people who fought against this kind of surveillance and today it's the feeling that's being used to give reason for implementing measurements like this. I mean this is obviously not about stopping attacks to happen. This is not about measurements to prevent stuff from happening. These are all measurements that are being implemented and established in other countries and they're not being effectively put to use. But in Austria yet we still kind of actively try to use this rhetoric to justify measurements that were undertaken. We're going to hear another quote from our minister from his last few days in office. We know today that the next attack is being planned. We don't know when and we don't know where. And this is also very typical. It's about protection from very abstract threats instead of concrete, evident, driven attacks. And this is how laws are being passed against potential attackers. They're not concrete. It's about people who are not actually giving any reason to be planning an attack apparently in the abstract they're being dangerous. So in the new... agreement, the new parliamentary agreement, it says that there needs to be measurement that you can undertake before stuff even happens. So you have to want to start limiting electronic measurements of communication for people who are being potential threats. So I mean, we could all be potential threats. You can only say that you're against this kind of security package and based on our minister of inner defence. You're basically an attacker onto the democracy of Austria. And the problem with these kind of databases of potential threats is that it's really hot to then afterwards be taken out of these databases. Like, how are you going to prove that you're not a threat any longer when you were there, being put there in a first place on very flimsy kind of evidence? So we've talked about this kind of abstract, yet very big, bad threat. And the measurements that we want to use against this are very small. We're going to watch another video. We just basically want to close the gap. We just want to close the gap in our measurements of surveillance by using digital means.  And then everything is being safe again. That's the thing with the technology. We a lot of times reach the threshold of understanding technology. And it's kind of like making family policies and not really understanding how families actually work. In this case, it's unfortunately not leading to people stopping to make more statements. They are kind of more fired on to do more. We can see more. I mean, we could basically have more people in cyber crime that could technically look at how this looks like. All right. Thank you very much. I mean, I'm not the really good technical expert, but I could... Yeah, sorry, I can't explain. So Peter Gridling, who is the boss of the protection of the Constitution, basically the boss. And we should remember this name because he's going to come up later. Very similar is the Vienna head of the police. So you could look into the software being used. And you could basically look into people's private homes. And his response to that is kind of like, well, I mean, these are technical measurements. I mean, you can't say that these technical measurements aren't possible to execute. And they're basically showing a bit of technical ignorance. You basically can't have a fact-driven conversation with these people as they do not fully understand the technicality of things. So their attitude towards this is more towards of a toy, where they're like, oh, why don't you just give them the toys? Let's just not talk about it for longer. Let's just... Now we're going to look at the former minister of justice. So if the boss of the Bayfadi thinks these are important measurements, you just have to undertake them. I mean, he's like cheering people on to give more applause. Basically, one reacts towards the wishes of the constitution safety. And he cannot give a response on how this is supposed to technically work. But don't worry. It is for me very curious how the state permanently, where everybody swears an oath on the constitution, that they're being basically accused of misusing the kind of data. I mean, basically just trust the government because they never misuse data. It doesn't exist, does it now? I mean, there's multiple examples of data misuse. I can give you one example where one police officer gave a woman that he liked information and data on the current men that she was seeing and on his background. And I mean, no, there's no misuse on the state level when it comes to personal data. I mean, you shouldn't just trust the state and the government. I personally wouldn't trust anybody who defends themselves with arguments like those. Here again, this is Werner Armand, the security speaker in the parliament. He says data protection must not be misunderstood and turned into a perpetrator's protection. But data protection is a foundational right that protects everyone, including perpetrators. And there's nothing to be misunderstood about it. And secondly, those permissions are to investigate and they are directed against either both those that are accused and those that we don't yet know. Now, the debate on surveillance is characterized by a very diffuse or surprising competition logic. It cannot be that... And here comes a football analogy. Champions League, regional league. Champions League and regional league. Other countries also have those surveillance capabilities and we're not going into competition with other countries, but we're going into competition with terrorists. So we need to apply methods that also the criminals use, but perhaps that isn't what he meant to say. So there's a strange interpretation of democracy. So here he states that security is more important than politics. I don't want to not have a political discussion about this and I do not understand why it needs a political agreement on this, or political compromise. There was a debate and then in 2017 elections, there were two topics in internal politics or internal security politics. So the FPO did not take any stance in this debate and he said he didn't want to draw this delicate topic into the election and he does not want to use it to distinguish from the conservatives. So here the ÖVP tried to make people feel good and they stated that... and they made it seem like they were against it, but they continued with it. There's still no transparency law under the new government. Before the elections they were opposition party and they were against it and they declared it to be the end of the legal law-based state. So here the topics Islam, migration, security and surveillance are mixed up in order to create insecurity and create emotions. This is Harald Wilinski, a high politician from ÖVP and he's an EU delegate. He wants to show that he is a security party but not a security party. He's in the opposition party and he speaks about the ÖVP, which was his opponent then and now is his coalition partner and he says that they want to be a security party and really they are only a surveillance party. After the National Security Council he stood before cameras because the left wing succeeded and all of those items in 8 months we took them off the table. With 220 people we submitted 18,000 comments and that was the biggest in Austria and with a long distance. Difficult for us was that this topic needed to be discussed in Austria. Now we've had multiple journalists that wrote about it in their newspapers. Even Boulevard papers were talking about it and we are very proud that we prevented 10 of those 12 topics and now it is after the elections and the whole thing is coming up again. You can remember my statement from a few months ago and when I said it's an attack on the security to not do this. If we don't give those abilities to police then we have a few chances to find the terrorist networks. He repeats the accusations that he made in the beginning of this talk and shows you to anybody who thinks that these kind of measurements are threatening democracy so he thinks all of you are potential terrorists. Since very shortly we have a new government and when the coalition papers were released we released an analysis of the 180 pages and we color coded their relevance towards cyber security and surveillance and we basically color coordinated by traffic lights. There is gaps in internet communication that are supposed to be closed. You basically can see the Trojan horse of surveillance lurking in the corners and that's not all. If you remember dieselgeras there is supposed to be a database where all of your reports from kindergarten over high school to university are supposed to be saved to then be made accessible for potential new employees in the future. For grownups this is supposed to be introduced within all e-learning classes and there being basically another bigger topic that is kind of above all of this. This is the third attempt to introduce a third Trojan horse run by the state and that raises the question is when have we actually finally won? When do they remember? The tough response to that is that civil rights are not defending themselves. In order to protect our civil rights our fundamental human rights we need to be aware, we need to keep up awareness and there only needs to be one moment of unawareness where that can be taken away from you. The FPU that back in the days was so much against surveillance is now in line. This is our new Minister of Inter-Defense Habat Kikkel. He's basically paraphrasing what the other guy was saying about how it's impossible that threats from outside have these capabilities technically speaking but the own government and the own police are basically not allowed to access the same kind of technologies to defend themselves. But they've also taken on another rhetoric. The one from the counterparty from the electoral campaigns. So in the first interview that he's given he was basically quoted saying if our security is doing well all of us are doing well. Funny enough the website itself that the news was released on is not even under HTTPS security yet. Oh the irony.  To come to a conclusion of this we would like to talk about our language. The language that we used to have something to be put against the kind of political rhetoric that's been going on. So what we've tried to really make sure is make clear that this is a package of surveillance and we successfully managed to set these as a rhetoric of the media. This is not a security package this is a package of surveillance. These are all surveillance measurements. So this changing of the narrative was what I want to conclude on because that I think is the aspect of this story that is maybe potentially for all of the people who are interested in this or even in the private life is maybe the most useful. The changing of the narrative that we need to make possible. We only, only win the debate on mass surveillance. If we change the subject. There's a lot of other measurements that can be undertaken that are a lot better and more effective for security while also still maintaining our own privacy. We need a fact based politic that is still in line and in accordance with our fundamental civil rights. We need to have all these measurements being checked towards their accordance with our constitutional rights and that's what we can thank you on. Thank you for listening. Applause from the audience. I don't think we have time for questions but we have an assembly in hall three right beside EFF in Edri. We're here until day three and even on day four for a little bit and we are a donation based association. So please support us, we need it. Thank you so much for listening to the talk, The Language of the Surveillers by Thomas Lohninger, Werner Reiter and Angelika Adenzama. The translations today for you did... Always 10,000. ...and Merle. Send us feedback if you have any at C3 lingo or at under the Twitter hashtag C3T.


If it is, I should be bleeding. You look better. Thanks. Hey, welcome back to our studio direction of Corbin. I'm Rick. You can follow us on Instagram, Twitter for more juicy content. Thank you to everybody's supports on Patreon. Follow us for your Twitter account. And subscribe and hit the like button. Yeah. And welcome back. Today we're doing a movie review. And we're in our car because we watched it on the phone in our car. Yeah. That's a little screen. No. Best way to watch a movie. Obviously just stepped out of Jawan. The highly anticipated second film of Shah Rukh Khan in 2023. It's directed by Atlee. And I think the story and screen was by Atlee as well. Yes. By the people as well. Composed by Ani starring Shah Rukh Khan. Nayan... What's their name for me? Easy for you to say. Nayan Thara. Wait. And Vijay Sarapathy. Yogi Babu. Did you see Yogi Babu? No. Was he in this? Wow. Or did he get cut? And obviously other people because I think obviously the whole cast is not here. But obviously it's Shah Rukh Khan's film as you all know. Just stepped out of it. Obviously since it just came out we're going to do a first non-spoiler review. If we want to get some spoilers we're going to get to spoilers. We will let you know before we do that. We shall not ruin it for you. Rick, your initial thoughts of Jawan. So this was tremendously disappointing for me. I am extraordinarily disappointed. So yeah. Didn't like it. Tremendously disliked it. Yeah. Tremendously. I have... I can only think of maybe two things to say that I would find complimentary about it because there's so many other things that are so tremendously disappointing. So yeah. I really disliked it.  I didn't love it either. If I was to give it a gray to be... And I know it'll be much higher than regardless of what my score is. I'm going to be higher than yours. Probably more the 65 range out of 100. If I'm doing that maybe closer at parts maybe 70. It just depends on the part. So I enjoyed it much more in parts.  Which is obviously a genre that we still are not accustomed to. And also next time we have one of these films I'm going to go regardless of when it is I'm going to go to whatever showtime has the most people. Yeah. Because I think that's also sometimes with these style of films because they're not our normal cup of tea obviously in terms of massy kind of films. It helps when you have a crowd that's also enjoying it obviously.  But obviously definitely didn't enjoy as much as I've heard other people have enjoyed it for sure. I know I've probably enjoyed it more than Rick did. Yeah. But we'll get into it obviously. Did you enjoy... What did you enjoy first? I appreciated the... I mean, Atlee can clearly with the team of his cinematographers...  Sorry. I want to make sure your head's not cut off. Okay, good. Atlee clearly with his team of cinematographers can do some things that are extremely intricate technically with cinematography and visuals. Got you. Yeah. You didn't enjoy any of the fight scenes though? I liked... Logic apart. No, no, no. I was logic apart on the fight scenes especially in regard to something that's revealed in the very first fight scene that happens which I liked and felt maybe that's a particular direction we were going to justify some of the things that we were going to see. But no, there wasn't anything particularly stand outish for me with the fight scenes. Yeah. He didn't like the... Without giving it away like there's one... The interval. There's an interval scene. Yeah. I enjoyed that interval scene regardless of like how it fell in terms of like the story of whatever. It was a very South Indian, messy. Even though I actually, in this, one of the issues I had with it is that it didn't go as South Indian, messy as I would have liked it to in terms of the fight scenes. So like in certain... We've seen some South Indian, messy fight scenes obviously a lot. A lot. And like let's say if there's a hammer, that hammer's going through somebody's skull and we will see it. And I feel like we didn't get that. I was waiting for some like, some fun bone breaks, all this kind of stuff and I... No, from my money that came with Jailer. Yeah, yeah, absolutely. Obviously, a thousand percent enjoyed Jailer. That was a lot of fun. And at times I did enjoy this film for the messy moments and stuff like that but it never went far enough in terms of... I feel like it was like a watered down South Indian mess film. Yeah, that's a good description, yes. Obviously, story aside of certain plot points. No, when we were just specifically talking about the action sequences and the stunt sequences I would absolutely say that's why they just never really engaged me because the last time that I saw that on a big screen was not too long ago with Jailer and that Jailer's just from start to finish just such a fun, wonderful movie. Yeah, and like I said, I enjoyed parts of the... There's fight scenes and there was some comedy that I appreciated but I wanted the fight scenes to just be more epic and I felt like maybe they were watering it down for the Hindi commercial audience maybe and I was like, well, if you have a South Indian director, why not take advantage of that because that's one of the things that did disappoint me even though I didn't...  I just... I wanted... if it's a South Indian director, South Indian production shall we con one to be a South Indian superhero basically? Yes. Why not go full throttle? Especially in the fight scenes is what I'm talking about. I agree with you completely. Even though my favorite was the interval fight scene, I liked that one a lot but what about the performance? Not that there was like an Oscar-worthy performance. What did you think about the performances? I was more disappointed with performances than anything that would have impressed me primarily because so much of the script was just dreadful and a lot of the performances were just performative. I didn't see anything like, again, comparing it to say jailer for as as massy and big and over the top there was still some level of... because the script was better there was a level of believability of these characters other than just being like I said at the outset I just... this didn't feel any more connective to me as a human being than if I was watching Micah play a video game and I think this would probably be... and it's not neither of our favorite genres similar to and I've never seen all but one of them and it was one of the older ones like Fast and Furious or Expendable, we saw the trailer for the new Expendables movies which was absolutely the right film to put as a trailer before this movie they knew their audience for the trailer neither of our favorite kinds of movies like action is usually never... even though I can appreciate some good action obviously and there's some... if it's done well I can appreciate it but it's never going to be my favorite style of film it would be my least favorite... if someone said what's your least favorite style of film I would say it's just brainless action films like Jason Statham I've seen one Jason Statham film and that's why I've never seen another one they just... I'd rather watch Grass Grail and this was... this was... similar at least I think because I've never actually seen those movies but like in terms of... if you're trying to think of any kind of logic you're just... you're already dead to rights or... or... yeah logic in every way not just logic in the terms of the action and the stunt work and things of that nature but any logic in terms of things that happen in the story any logic in terms of the relationships that people have any logic that happens in terms of continuity any logic that happens in terms of believability with makeup even... there were points where I just was thinking to myself again... how are you allowing that CGI with Red Chili's name attached to it and the amount of money that an SRK film can garner I just... yeah it just... missed it every level for me A lot of the songs were good but we'd seen most of them already I think it was... two I guess and there were parts like they left out of the stuff that we saw in our reaction as well there was quite a few cameos yeah there's some cameos there's some cameos and then there's like... VJ Sadapathy's character who plays the villain in this which is not a spoiler yeah he's in the trailer and you would assume he would be the villain from it I thought he did fine like I said you did? yeah I did I was disappointed I wasn't expecting his normal gravitas oh no I wasn't... I didn't anyway my expectations might have been lower because I was expecting action Patan which I think this had actually had better action than Patan and better CGI I liked Patan much better did you like this more than Patan? it depends because the second half of Patan was extremely disappointing for us and the CGI was awful it was but I could sit through the first half of Patan again easily I enjoyed the first half of Patan yeah like I said I didn't hate this movie as much as you hated it so it's different both have their flaws for sure and both aren't totally my style of film either so I'd much rather see Shabrakan in a full-on romance role or something like Dawn II that also had action flaws too though yeah but it is head and shoulders for me above this well that wasn't trying to be fully massy either I'm not sure mass is one fully our thing but definitely not your thing well is Jailermass? I think you also gave Jailer a lot more forgiveness because it's Rajnikanth I'm not trying to say this is anywhere Jailer's a much better film than Jailermass I agree and it is mass? yeah I mean Rajnikanth is the king this movie star of mass that had just a little more groundedness though than a normal mass so I think normal mass you're not so is normal mass basically expendables? I think so you guys can let us know if I'm wrong but most of the mass films that we've seen you have not been a huge fan of I'm not trying to defend them if what it means for a mass film is to be like say for example a Jason Statham film where all logic in every sense of the form and any attentiveness to anything of artistic merit is just kind of thrown out the wayside because you're just going to have a banging good time in some way that is on par with say a video game then yeah I'm not a massy fan yeah because I think the point of mass films is just entertainment and I don't think there's actually anything wrong with that it's just some people is not obviously their cup of tea understandably but I know I have film buff friends who are like the biggest film buff I know that like they'll break down every single part of a film but they also love fast films I know somebody who their favorite kind of a film was a Jason Statham film and I went to them with that's the one film I went to and I just could not it's not everybody's cup of tea because obviously people look for different things in film some people just want escapism and entertainment and some people obviously they want more from that from the cinema obviously you are one of those that wants more from your cinema but I don't have any problem with and I do appreciate films that are entertaining I just don't know why anyone would find this kind of a film to be entertaining well I think there's I wouldn't agree with that I think there's entertaining parts of this film is that a full-fledged package that I love and I think it's like a like RRR would technically be have mass in it I wouldn't classify that as a full mass just because I think SS Rajamouli is just really gifted at his craft in terms of like making mass good and entertaining because there's mass moments like the fact that a junior NTR can carry Ramhturan on his shoulders and then killing people like no logic obviously massive stranding of credulity in that respect but you've earned at that point for me you've earned the right to do that kind of thing so for example in this in addition in addition no I won't in addition to the lack of logic in so many respects one of the other things that this film does ad nauseam is try to make you know try to cash in on emotion where you've done nothing of a deposit in any way shape or form into the audience to justify the fact that you're going to try to cash in on that emotion other than you're just going to placate and that is especially in some regards which we'll talk about in the spoilers in a second where it was almost insulting to me that you're trying to now tap into my emotions when you've done literally nothing to invest in them with anything coming close to being empathetic or even humanly interesting so that's another part from what I've found of mass films is not only mass action basically a lot of times no logic everything's basically just for entertainment or to get an emotion out of you everything that is the purpose not to make you believe it just to get it out of you which to me you know trying to evince an emotion out of someone without it being honest is which is one of the reasons that the problem I had with Jailer even though I know you didn't have the same problem is I felt they were doing that with Jailer which they didn't do for most of the film at the end that's one of the issues I had this one obviously the entire time they were doing it and so maybe it would have fit better but that was one of the reasons I didn't like it I felt they just did that to get the emotion out of me I know you didn't have that issue with that yeah I know what part you're talking about and I didn't think it was manipulative but I feel like that is another aspect of mass but at least they saved that to the end and tried to justify it with the fact that they had a relationship like I said ShowerCon had some funny moments he obviously it's no spoilers and he plays a few characters and that's in the trailer but it's just overall I had an okay time I know you did not but I mean you probably had a better time than Theory though no can you say that? yeah I could say that they're little positives but I didn't have the kind of expectations for that maybe for the next mass films we should go in with less expectations I don't know because I had high expectations for Jailer and it exceeded him for me that's true maybe this just was a bad movie maybe you guys let us know what you thought about the film and that's one of my big issues I think if this had been a South Indian film it might have even been better because it felt almost watered down that's one of my biggest issues if I'm going in for a big mass Danish film I want to go in for a big mass Danish film kick an ass and obviously bone breaks at times, not all the time there was moments that I did enjoy that they were watering it down for the Hindi commercial audience either that or just trying and not succeeding yeah maybe it's a South Indian director so I assumed it was somebody else telling him because he knows how to make the mass films but anyways, obviously done with the non-spoilers we'll go into the spoils now come back you can let us know and then we're going to get into some spoils that's just what we wanted to talk about I guess the first thing I was never looking for logic there's just one moment specifically that was like that is insane that's what you decided to go in when you fell from the sky that was insultingly stupid there's so many different ways you could have done it it's just more believable it just basically lets you know audience, we think you're complete idiots and we don't care but the fact that he fell from a plane whatever the distance was it could have been 10,000 feet internal velocity at that point but the fact that he won the branch breaks his fall that would have cut him in half but then water is essentially like I saw a real of a guy doing a dive off of a cliff that was about 35 feet high and he hit the water and broke his back at 30 feet he did get incredibly hurt and then he laid there for a month and got up and destroyed I think it was six months as he laid there and was able to get up and destroy everybody but that happened in Batman they broke his back he was becoming the incarnation of a god that's what justified it for me in the beginning at the very beginning I was looking for the justification we didn't know what had happened how did this guy bleeding out laying there for a month suddenly have the power to destroy all the people that had attacked the village and it was because the guy had been praying to God and said prove that you're not more than just a stone and he had become imbued that for me was the only justification in the film there was a bunch of moments obviously but I was looking so can I bring up the ones I dislike? if you can give me a justification that's not the point of this film one, if you're going to show somebody naked just show them naked, don't do the stupid I'm going to blur it for you well, the censor board gosh anyway if so did you know that you could find out someone's pregnant just by checking their pulse? I had no idea that's another one we assume you don't know how people get pregnant you're going to have someone take her pulse and look at you and say she didn't just faint, she's pregnant good grief um I also didn't know you could raise a kid in prison that was new to me good grief I don't think we need to go down all the times because once again, if you're looking for logic in a mask I think you've already lost I'm not trying to defend any of them the most egregious one I thought the pregnancy one was just hilarious seriously, the most egregious one no, at first I really liked the direction things were going on the train and the fact that he was a Robin Hood who was doing what he was doing and I thought, oh my goodness, this is actually like a legitimate point about the farmers I wasn't expecting this is this thing going to have some balls? is this going to be like an action film that also talks about some of the deeper realities of what really goes on in the world like Dark Knight it not only didn't it then used those issues as just a point of being part of the story and it ended to the point where it just became insulting not just to intelligence but insulting to the actual issues themselves they were used as just plot points to continue the film rather than legitimate stories which they had done on the train at the beginning and that deeply bothered me because they're very real instances where I thought, you know what, how cool would it be I was thinking this at the train segment and he's this anti-hero like Veefer Vendetta or even the Joker I consider an anti-hero who is wanting to correct some of the wrongs he sees in India and then what if SRK came out after the movie opened and said, I've created an organization and all of the proceeds from this film are at least what I've made on this film since I'm worth nearly $1 billion are going to go to the issues in this film in some way, shape or form and actually cross that line between entertainment and actually having your message become something that's impactful and changes the lives of the people that you're using in the story as part of your plot line so I guess I would be disappointed I was just trying to remember what I wanted to talk about in spoilers there's something specifically but I'm trying to continuity, no, no, it's not a negative I was just wanting to talk about a kid raised in prison no, Rick, stop no, I'm genuinely... no, no, no, no I'm saying those things to save the triggers of thought no, um... it's nothing to do with I actually would love to see VJ Sattapathy be Santa Claus nothing to do with the movie I know he's doing a Merry Christmas movie obviously that comes out later this year I think he would be a great Indian Santa Claus you look great I think he would be a great... I love his look at this his look with the beard was epic, he was handsome I actually loved in terms of just some of the other things I would love ShowerCon to come out as the old look ShowerCon in like a full... maybe when he's 20 years from now when he's older and do look like Superstar Rajrakanta just kicking ass because I like that look a lot Deepika's role I thought some of her action was cool but I wanted her to do more I wanted her action to be... that's one of my main things like I've said, I wanted some of the action to just go farther because you have one, Red Chillies and two, you have a South Indian director they know how to do mass action and I just... I wanted to see Deepika crackin' heads so I wanted some bad assery I actually thought the girls would be involved in more of the bad assery to a certain extent too they were, they just... you didn't show them as bad asses maybe I wanted it to I didn't hate the movie I know Rick did I didn't hate the movie but I wanted more I definitely wanted more in terms of just from what we've seen Jailer, right? this is a thousand percent bigger than Jailer in terms of the production size obviously but you think you could do more then, right? but sometimes less is more, right? no, and that's the thing for me is because I so appreciate Shahrukh Khan and to know he has full creative control over every single thing it's Red Chillies, that's his company it's his name to do the film and have it be done and walk away and say, yeah, I'm happy with that is just shocking for me I've already heard a lot of people really enjoy this film so it might just be an us thing that just don't get this style of film it's possible, obviously we've given you our point and we're going to be honest it will never be not be honest, it's happened many times something extremely popular in terms of Pushpa KGF2 Patan, even though we appreciate parts of Patan we didn't love it as much as everybody else did I think the closest things would be where everybody was jumping up and down raving about Pushpa and KGF2 and that hopefully I hope that's one of the things you love about us is that you know when we say something positive and affirmative we mean it because we will tell you when we really dislike something and it's never with the intent the movie, right at the beginning it said, hope you enjoy the show and I said, I really hope so because you don't go into a film hoping it's going to fail unless you're just a mean person and the movie is made by somebody that you truly detest I go in rooting I wanted this to be good so you guys can let us know what you thought about the film if you liked it, if you didn't like it why we're idiots as always it all helps the algorithm so just let us know down below