The Equitable Society presents this is your FBI. This is your FBI, an official broadcast from the files of the Federal Bureau of Investigation presented as a public service by the Equitable Life Assurance Society of the United States. To your FBI you look for national security and to the Equitable Society for financial security. These two great institutions are dedicated to the protection of you, your home, and your country. Tonight's file, The Strange Extortion. Hardly a day passes that some person of large income or great wealth does not receive a letter demanding that he pay the sender a certain sum of money or suffer the consequences. The usual implication is death to himself or some member of the family. True, most of these extortion letters are written by cranks who never carry out their threats but the FBI must investigate them all and quite often the letters are the real thing. Tonight's case from the files of your FBI involving attempted extortion is one of the most extraordinary stories of its kind on record. Lintrock was a wholly appropriate name for the old secluded Long Island estate for it not only described the volcanic outcroppings about the place but it suited the character of the despotical woman who ruled the Coldray Stone House with perpetual ill temper and a passionate contempt for all under its jagged roof. Although Letty Bradford could seldom leave her bed, her irascible spirit haunted every room and had long since made Lintrock a house of mutual hates. It is now one minute after nine o'clock in the morning. Letty Bradford reaches for her stick and...  About time young lady. Good morning Mrs. Bradford. Nearly two minutes after nine Janet. I'm sorry. That's no excuse. You know very well I want my breakfast at nine o'clock and nine o'clock doesn't mean two minutes after nine. Yes Mrs. Bradford. I suppose you stopped to poison the orange juice. No Mrs. Bradford. Don't tell me the thought hasn't occurred to you. No Mrs. Bradford. Of course it has. It's occurred to all of you. And why should it? Don't question me and don't look at me that way.   You're too eager to get your ungrateful fingers on the money I've left for you in my will. I don't expect any money. You've always paid me for my services. Inefficient as they are. Shall I pour your tea? Don't you always? You want me to drink it, don't you? You said for me to pour it. There are some poisons that cannot be detected in the body aren't there? Yes there are several. Hmm. I won't drink the tea. Take it away. Take it away I say. As you wish. Well don't stand there tapping like a woodpecker Charles. Good morning Mrs. Bradford. Good morning Janet. Ha. Another Judith. I beg your pardon Mrs. Bradford. Take the tray Janet. How long have you been my secretary Charles? It will soon be 10 years. Hmm. You must have robbed me of a tidy sum in that length of time. If you think I have why don't you have me arrested? Nonsense. I admire your ability to hide your pilferings. What have you got there? The morning mail of course. Oh don't bother me with mail this morning. Where is my adoring niece? Miss Daryl is. I know sleeping it off under a pile of ice bags. Miss Daryl stayed in New York last night. Well you have ice bags there too don't they? What's that? A letter addressed to you Mark confidential. Confidential.  Open it. I didn't want to without your permission. Open it. Mrs. Bradford. Well. It's an extortion letter and they threaten to. Well don't have a stroke about it. What they threaten your life unless. Unless what? Unless you pay them $30,000 by noon tomorrow. Hey who $30,000. You are to wrap up that amount in bills of small denomination and see that the package is left in the alley behind the North Shore Bank building in Island City and say nothing to the police or. Or they'll bash my head in I suppose. I'd better get Judge Madison on the telephone right away. You'll do nothing of the sort. Some crank nonsense. Throw the letter away. Put Mrs. Bradford. You heard me throw it away. Very well. Charles wait a minute. Yeah. Why should anyone ask for $30,000? Why not $25,000 or $50,000 or $100,000? Why $30,000? It is an odd amount. There may be something to this after all Charles. Get Judge Madison over here right away. I wouldn't be surprised if all this weren't some scheme of your own Tom Madison. Oh my dear Letty. Of course I could use $30,000 to good advantage but.  As executor of the estate you'll be able to milk it for a whole lot more than that. Come now my dear. This is a serious matter. What's serious about having my head bashed in? That would be a happy event for all of you. Oh please please my dear. If the letter is a genuine extortion letter you have until noon tomorrow. And you may rest assured my dear. Before then I'll see to it that you have ample protection. I don't want a lot of to do about this in the papers you understand? The FBI doesn't operate that way. What does the FBI have to do with it? This is a federal crime and I must report it to the FBI at once. Judge Madison drove swiftly into New York and went directly to FBI headquarters. Where he reported the case to special agent U. Barnes. And here is the letter Mr. Barnes. Uh-huh. Now this looks like the title of stationery ordinarily used for social correspondence. And whoever sent the letter was careful to use a typewriter. A typewriting can be as incriminating Judge Madison as handwriting. Each set of type leaves its own peculiar mark. But they don't necessarily prove who did the typing. No but it's a good clue anyway. Oh yes, yes of course. And who occupies the house with Mrs. Bradford? Besides the servants there's Mrs. Bradford personal nurse Janet Smith. Well what do you know about her? And not much except that she has attended Mrs. Bradford for three years. Single? Yes. A young man calls on her once a week I believe. Well what's her attitude toward Mrs. Bradford? Uh frankly Mr. Barnes no one has any real affection for Letty Bradford. Well for a mere description of her that's understandable. Who else lives there? Her secretary for almost 10 years Charles Forbes. Single about 34. Does Mrs. Bradford have any children or other relatives? Only niece Daryl Bradford about 27. Very attractive. Also single? As Daryl says she's still playing the feed nightclub style. Has a generous allowance I suppose? Not always generous enough. I've had to clear up her gambling debts from time to time. For large sums? They've varied in the past. I say past because three months ago Mrs. Bradford's war she would never settle another one. Now what about the servants? Well there'd be no reason to suspect any of them except to well... Except whom? The chauffeur Floyd Parker. He likes his drink a little too much and occasionally he's disappeared for two or three days of time on what he calls a little bottlenecky. I see. Mrs. Bradford says she had a row with Floyd on the subject two days ago and fired him. Anyway Parker's gone. More late. Yes Barnes. You get a complete description of Floyd Parker from Judge Madison and start trying to locate him will you? Right. There are a couple of angles I want to go out on for a while Judge. Would you be good enough to meet me this evening at the Bradford house? Certainly. And please see that everyone's there including Darrell Bradford. Darrell. What's good about it Charles? I'm sorry I had to call you. You didn't tell anyone where I was? Certainly not. Thanks. Now why should I have to come all the way out here because that old you name it got some kind of crazy letter? The FBI agent wanted everybody here. FBI agent? Yes. He's been all over the house for the last two hours. He's in the library now and he's already fingerprinted all of us except you. What? Yes. You mean he? He suspects that one of us? I guess it's their job to suspect everybody. Mr. Barnes, the agent, ask me to have you come into the library as soon as you arrive. All right. I'm Darrell Bradford. They say you want my fingerprint. Please if you don't mind. Were you expecting me to object? Do you? Why should I? It'll only take a moment. Now press your right fingers on this ink pad please. Good Lord. Wonder if I've robbed any faith lately. Well probably not or you would have paid off your gambling debt to Nick. Now press your fingers on this card here. What do you know about Nick? Well he's a dangerous man to owe $30,000 to. Now the left fingers please. All right so you know about it. But I didn't write that letter. I didn't say you did or you didn't. If I didn't, who did? I haven't found out yet how many people know about your debt. And a lot of people including you would benefit by Mrs. Bradford's debt. Have you finished with me? Well for now yes. Oh please send the nurse Mrs. Smith in will you? And I'd rather you wouldn't leave the house. Very well. You're in charge. Barnes speaking. This is Morley. Any trace of the chauffeur? I've also put out a five state alarm for him in case he decided to roam. Good. I'll be here for a while yet thanks. Well this is a sheet of your stationery isn't it Mrs. Smith? Where did you get it? Out of your room. And I guess it's mine. Why? Well the extortion letter was written on a sheet of paper exactly like this. And that makes me guilty I suppose. I didn't say so. If anybody wanted to get $30,000 for Mrs. Bradford it probably would have been. Then you knew about Daryl Bradford's gambling debt? Charles knew about it. He told me. I thought he was supposed to be a confidential secretary. Charles gets sort of confidential with me too Mr. Barnes. Oh excuse me Mr. Barnes. Oh yes Charles. Judge Madison called over the other phone a few minutes ago. Said he'd been detained but was coming right on over. Thank you. Oh that's all for now Mrs. Smith. Charles. Yes. Do you recognize the typing on this sheet of paper? Well it it's the same style I think is as the typewriter I use. That's right I typed this on your machine. What for? I mean... Well it's just possible that under a microscope it'll exactly match the typing on the extortion letter. Look Mr. Barnes. I didn't have anything to do with it. We don't reach conclusions until we get all the facts. Why should I try to extort money from Mrs. Bradford? I'm well and taken care of. I've been very well and... What? It's Mrs. Bradford Janet. She's been shot. Mr. Daryl. I'm coming. We momentarily close the equitable society's presentation of the Federal Bureau of Investigation file on the strange extortion. We'll return to this case in just a moment. A quarter of a century ago a great American President Woodrow Wilson saw the need for world cooperation. He urged the nations to get together to drop their rivalries to form a united front for world peace and security. Today the ideals of this far-sighted leader are an inspiration to those who are planning to banish injustice, war and aggression from the face of the earth. Members of the Equitable Life Assurance Society of the United States will be proud to learn that this great advocate of international cooperation was a member of their society. Like Woodrow Wilson, this society also stands for security through cooperation. In fact the Equitable Society is an excellent example of the advantages of cooperation. Instead of trying to struggle with their security problems alone and unhated, three and a quarter million Americans have joined forces in the Equitable Society. Instead of continually worrying about the financial future of their families, Equitable members have shifted that burden onto the broad shoulders of their society. The peace of mind which they gain makes them better workers, better fathers or mothers, better citizens. Yes, by serving its members, the Equitable Society serves America. So remember that name, the Equitable Society, the Equitable Life Assurance Society of the United States. And now back to the file on the strange extortion. In the case of Letty Bradford, mailing the extortion letter was a federal offense. But when Mrs. Bradford was found apparently dying of a bullet wound above the right temple, special agent Ewell Barnes called Inspector Blanton of the Homicide Bureau, who took charge of the house and posted men to see that no member of the household tried to leave. Agent Barnes, however, continued to conduct the investigation. Letty Bradford's doctor, Inspector Blanton, Barnes and the nurse Janet Smith, herself under suspicion and connection with the letter, have been in Mrs. Bradford's room for some 30 minutes now. Judge Madison, who arrived shortly after the shooting, is standing outside in the hall with Charles Forbes, Mrs. Bradford's secretary. The door opens and Barnes steps out. Well, Mr. Barnes, Mrs. Bradford, the bullet didn't penetrate as we thought at first. The pistol was evidently fired at such an angle as to cause only a deep scalp wound and severe powder burns. You mean she's unconscious now, but largely from shock. She'll live. Oh, Judge Madison, did you ever see this gun before? Why, yes. Was that the pistol that's found on the floor behind her bed? That's Mrs. Bradford's pistol, Barnes. Mrs. Bradford. I didn't know she had one. Yes, Charles. I bought it for myself three weeks ago. Said she wanted one for protection, so I humored her. Thank you, gentlemen. You know where I can find Mrs. Darrell? Oh, yes. She went downstairs just before you came out, sir. I saw her going toward the library. Thanks, Charles. And Judge Madison? Yes. Inspector Blanton says no one is to leave the house just yet. If you'll excuse me now, please. It's not my fault if she doesn't die. I didn't do the shooting. What? Well, if she lives, you'll just have to give me more time. I can't raise $30,000 like an umbrella. All right, do anything you like about it. I didn't intend to eavesdrop, Mrs. Bradford. I didn't call Nick, Mr. Barnes. He called me to hound me about the money. I told him what had happened and I... Oh, all right, believe what you like. I'm on my way to New York. I merely stopped to give you the doctor's verdict. Your aunt will live. Good night, Mrs. Bradford. Good morning, Barnes. You don't look very happy. I just mixed up, I guess, Mawley. No trace of the missing chauffeur yet. Not yet. What about the pistol? There are no fingerprints on it. I can't understand anybody leaving it behind the bed in the first place. When you got to her so fast, I don't see how they had time to escape. Well, they didn't use the window. That's a cinch. Do you suspect anyone in particular yet? Look, Mawley, it's easy to suspect nearly everybody out there. Most all of them have acted funny about one thing or another. A nurse about the stationery, the secretary about the type, Darryl Bradford, about $30,000. And they all stood to gain by Mrs. Bradford's death. Yes? Here's the laboratory report on the extortion letter, Mr. Barnes. Good. What's the verdict, Barnes? It's very interesting. The extortion note was typed on the secretary's machine. The only fingerprints on the letter are his. Oh, wait a minute. Here's something else. Also found on the stationery were microscopic traces of purple suede fuzz. As if it had been handled by someone wearing purple suede gloves. I'll take it. Barnes speaking. Oh, hello, doctor. Yes? Yes, I see. I'll be there. Thank you very much. And this is Bradford's doctor. He wants to keep her quiet for the rest of the day, but says she should be able to talk to me by tonight. Good. In the meantime, I'm going to do a little checking on Nick today. And if you get any word on the chauffeur, call me at the Bradford house tonight. Right. Special Agent Barnes spent the rest of the day investigating the movements of the gambler Nick and his men during the past 24 hours, but could uncover nothing involving them with the shooting or the extortion letter. Shortly after dark, Barnes forged his car through a rain and windstorm sweeping Long Island up to the Bradford house. Letty Bradford could talk, but claimed she could remember nothing that happened. Barnes then assembled the others in the library. Charles. Yes? The extortion letter was typed on your machine. But, Mr. Barnes, I tell you- And your fingerprints were also found on the letter. Of course they were. I read the letter to Mrs. Bradford. I had to handle it to read it, didn't I? And Miss Smith, your fingerprints were not found on the stationery used. But there were traces of fuzz from purple suede gloves. I never owned a pair of purple gloves in my life. And Mrs. Bradford was shot with a pistol which you say you bought for her, Judge Madison. Good Lord, Barnes. You don't think I- I'm not accusing you or anybody else here of anything, Judge. I'm merely setting down some facts and I- Excuse me for butting in, Barnes. Morley, I thought you were in New York. Well, I thought I'd better bring him out instead of phoning the police found our men. All right. Come on in. Parker. I don't get the idea of all this. Are you Mrs. Bradford's chauffeur? Mrs. Bradford's ex chauffeur. You're just the man I've been waiting to have a talk with. Will you come into the other room with me, please? Thirty minutes later, special agent Barnes emerged from his talk with the chauffeur, whispered something to Janet Smith, the nurse, who immediately set off upstairs. Then Barnes called Judge Madison to one side. Well, Barnes? I think I have it all cleared up now, Judge. Parker, the chauffeur? No, but he was very helpful. He- he knew something? Yes, something that completely clears Ms. Darrow, the nurse, and Charles. I was finding it awfully hard to suspect any of them anyway. Why so? Well, Ms. Smith wouldn't have been so obvious as to use her own stationery. The same reason Charles wouldn't have typed the letter on his own machine. And Ms. Darrow? She needed $30,000 all right, but she's too intelligent to have demanded a sum which everybody, including Mrs. Bradford, knew she owed to Nick the Gambler. That sounds reasonable, but... I think I found what you want, Mr. Barnes. Yes. I'm afraid you have, Ms. Smith. Judge, I think you'd better come upstairs with me. All right. Mrs. Bradford? Well, what are you and Tom Madison up to? When you fired Floyd Parker three days ago, you gave him a handsome sum of money to soothe his feelings. What if I did? It's my money. You also gave him a letter to mail. A letter addressed to yourself. What are you trying to say, young man? Are these your purple suede gloves? Well, I... Oh, certainly they're mine. What are you doing with them? The person who wrote the extortion letter used Ms. Smith's stationery, Charles' typewriter, the amount of Ms. Darrow's gambling debt, and wrote it while wearing purple suede gloves. What if they did? And furthermore, she sought to escape an uncomfortable death from disease, at the same time put the suspicion of murder on the beneficiaries of her will, whom she holds in contempt, by attempted suicide with a gun registered in Judge Madison's name. Well, Mrs. Bradford? All right. All right. I did it. It's all true. And I have only one regret. It didn't work. As a public servant charged with protecting the lives, property, and general welfare of all citizens, the FBI is just as diligent in establishing the innocence as well as the guilt of persons involved in a crime. In the case of Letty Bradford, there were five persons on whom the shadow of guilt fell. But Special Agent Barnes was not willing to arrest any one of them for the crime because of lack of sufficient incriminating evidence. Instead, his investigation was directed at removing from over them what shadow of suspicion was there. And in doing so, he discovered the person who was guilty. You'll hear about the disposition of this case in just a moment. But now will you join the equitable society and a salute to the American industry, which employs more men than any other except farming? An industry which is most typical of democracy and free enterprise because it is made up of many thousands of little businesses. A salute to the architects, engineers, lumbermen, the contractors, plumbers, electricians, masons, and carpenters who constitute America's great building construction industry. During the war, these were the men who built army camps and vitally needed factories almost overnight. During the postwar years ahead, this is the industry which will be the wheel horse of our national prosperity. Authorities estimate that the building construction industry will erect one million homes a year for the next 10 years and will give employment to four to five million men. Today, the need for more manpower is acute in this industry and it can be counted on to provide large numbers of jobs for ex-war workers and returning servicemen. For many years, the Equitable Life Assurance Society of the United States has been closely associated with the building construction industry. Equitable Society funds have made possible the construction of countless homes, factories, and business buildings. Every time a member of the Equitable Society pays a life insurance premium, he knows that his money is helping to make jobs for millions of his fellow Americans. For just as Equitable Society dollars were fighting dollars in wartime, so at all times, they are security dollars for you, your home, and your country. Because of her physical ailments and extreme old age, no formal charges were filed against Letty Bradford. Next week on the Equitable Society's presentation of This Is Your FBI, be sure to hear the adaptation of the forthcoming 20th Century Fox motion picture, The House on 92nd Street, relating the counter espionage work of the FBI and protecting the secret of the atomic bomb. Featured on this broadcast will be the original stars of the picture, William Ithe, Lloyd Nolan, and Cygni Hassel. The incidents used in tonight's Equitable Society's broadcast are taken from the files of the Federal Bureau of Investigation. However, all names used are fictitious, and any similarity thereof to the names of persons living or dead is accidental. Tonight's broadcast was directed by William M. Sweets. The music was under the direction of Frederick Steiner. The author was Frank Berries, and your narrator was Dean Carlton. This Is Your FBI is a gerrydivine production. And now this is Carl Frank speaking for the Equitable Life Assurance Society of the United States, and inviting you to tune in again next week at the same time for This Is Your FBI. Want to sit in on a thrilling court case? Well then join the audience of famous jury trials which follows now over most of these stations. This is the American Broadcasting Company.


Your Coca-Cola bottler presents Claudia based on the famous play and novels by Rose Franken Brought to you transcribed Monday through Friday by your friendly neighbor who bottles Coca-Cola Relax and while you're listening refresh yourself. Have a coke and now Claudia Yeah, every last bristle It's the last smidge of soap out of your ear What do you everything? No soap. No soap for the sake of peace Well, and that's my cue to get up Just because I have to get up at six o'clock in the morning doesn't mean that you have to get up, too I know I don't have to I just want to Dark and cold Hold your teeth and Hours yet back in bed and go to sleep.  You bet. I'm stubborn when it comes to you eating Let's drive all the way to Long Island on an empty stomach. Yeah, who said I said Besides I had no intention of it I know I know you're not gonna tell me that you stop off at some roadside place or other and that's a cup of coffee to Be had is in a diner. I'll tell you that. The best cup of coffee to be had is right in your own kitchen, my lad You need to walk off by themselves I Know you once you get started in that car. You won't stop for anything. You seem to know my own mind better than I do Of course, I do much better So I have everything all arranged darling. What's more? It'll save your time, too I take it. There's no point in arguing not at all absolutely none dress warmly David. Now you stick to your cooking and I'll stick to my dressing But I still wish you'd go back to bed. David, please put a sweater on underneath your jacket. I am plenty warm Now look, there's no point in talking sense to you isn't there? No, no point at all. Well, guess not You men consider it very smart to brave the elements unprepared. It's the height of achievement. Oh, I can see that I can see that if you want me to go to Long Island on a full stomach You better get out of that kitchen and boil them eggs. That's right.  Just an egg will do. Long Island's an awfully long way under there. I think I'll get there On two eggs and four wheels. Thank you. Well, they're already on the side of the stove, David The wheels are the eggs. Eggs. Oh, and water in the pan ready to boil coffee in the percolator So all that's left for it is just a perk for you. Mm-hmm. Does the coffee know that? Of course it does. I told it. No Do I or do I not get a kiss for being so organized? Don't sidetrack me. Which tie you like best? I have to drive all the way to Long Island. Be rad, I think. You better kiss me now because it'll have to last you a long, long way Oh, I think I could go to the North Pole on that kiss almost. Then get out of the kitchen or better yet get back in the bed And I'll get out of the kitchen. Nope. To the kitchen it is. If you're all ready, you can come along too You see you can be drinking your juice while the eggs boil on the coffee perk Well, you better give me a timetable to be sure I follow your schedule. All right, I will You know we're whispering so we won't wake up Mama. Oh, is that what I didn't know It would have been much simpler if you'd just let me sneak out without all this bother. It's not a bother. It's a pleasure Careful now it's dark Practically is the middle of the night You know the very last thing I expected when I married an architect was to have him going to work in the middle of the night As a matter of fact, I never thought of you going to work at all now that I think of it Is that supposed to be a compliment? Mm, in a sort of a way Well, here is the kitchen. Oh put on the light will you? Yeah, let there be light And there was like imagine David get your orange juice out of the refrigerator while I get the coffee perking You're so bossy at six in the morning orange juice is all strange David. There's not a pit in a carload Oh, what a pity. Oh No too early in the day for pommies puns for breakfast. I don't know if I like puns for breakfast. Oh, no. Oh, no Oh, yes. Oh, yeah Water for the eggs be boiling in the midst so you can put the toast in now Have you been awake all night figuring this out? No, not at all comes naturally to me Now in go eggs I'm starting to feel like a troop movement. There's no reason for you to be self-conscious darling I'm having a lovely time getting you underway Be something to tell our children about now. I'm glad I know the reason The coffee's about ready to percolate. Have you drunk the juice yet? What have you heard from the toast Just going down now. My you're not cooperating David. Are you going to have any? Oh, just give me a sip of yours. Um, it begins have a sip. Hey, that's enough. Hey, hey, hold Do you want me to break your egg? No, just put them in the egg cup. I'll eat them out of the shell. Okay one two There Now David tell me honestly isn't this nicer eating it eating at home than in an old diner by the side of the Road, I don't mind diners the company's interesting after all my work and planning such gratitude This gives you pleasure. I'm willing to cooperate. Well, that's very decent of you old chappy Well, I have a decent sort of fellow old chap here.  It is good. Hey, it's getting late. I'd better finish breakfast on the double No, no, please don't hurry eating there. I know but I'm eating roger in long island eight o'clock Please don't rush driving. Now don't start telling me how to drive. It's awfully dark out, David I bet there'll be some ice on the roads now. Now drive carefully. I always drive carefully. And call me when you get to Long Island. I certainly will not. Well, tell Roger to call me when you get there. Now, if you're going to sit here Worrying about me all day. I'm not going to be very comfortable. Do you realize that? Well, I don't intend to worry all day.  That's me Yeah, that's all I have time for David, you didn't drink your coffee. Well, you drank it. But the whole point was to see you out of decent breakfast You already I want a little measly egg. No one little measly egg is all I wanted. No coffee. Oh, you're impossible. Where's my coat? Put on robbers. I'm not walking too long island. They keep your feet warm. Well, they're bad for your eyes when worn indoors Oh, no, no, no, that's only a rumor. Well, I will not wear robbers.   Speak of you. I'm off. Oh, I'll come to the garage with you It's cold out now. You stay in the house.  I wish you'd stay in the house Stay in bed. Stay in the house.  At what?  I just don't see it. It's time for little girls to be in bed Not little girls who have little men to get underway. You're pretty smug this morning, aren't you? You blame me? David, you know when I first married you I was just dope You were? But have you changed? Have I changed? Have I changed? Well, I remember when right after we were married you had an early appointment like today And I got up to give you breakfast like today Now well, I remember the eggs were boiled hard as marbles and the coffee hadn't even started Imagine and you finally had to leave the house without a thing between your ribs for a day Me hot. That's all me hot.  I couldn't. I'm a man of strong character Well, anyway, I couldn't have stood me. You certainly were And I'm a man of strong stomach too. Doesn't have to be so strong anymore, does it darling? Now that I'm so organized I shall allow my character to relax and take a well-earned vacation. You'll do that Nice of you, ma'am Oh my arm is stiff from patting myself on the back Stuck? No, it's all right Oh Gosh, the garage is nice and warm. Feels good, doesn't it? Maskedoodle back to the house. Your duty and done. I I hate to see you go, David. Well, don't try and think of things to detain me You can say that after all I've been thinking about is making things easier for you. Well, you just keep up the good work Darling Thank you. You have been sweet Drive carefully For the umpty ump time I will drive carefully.  Go on start the car. I'm up against the wall Keys Do you have the keys, David? Of course I have the keys. I no need to be so snippy about it Uh, you know after turning on the ignition, David, you press the starter. Well, thank you for telling me. You're welcome Well, do you press it? You stopped cabitzing. Yes, I I pressed it. It's funny. Nothing happened Car must be awfully cold for a thing What's the matter? Should be turning over car.   Will you all right? I'm shot. I'm shot. I'm only trying to help you, David Say, what about the choke or the throttle thing or something? It's not the throttle thing It's a throttle and the throttle won't help. Well, then the gas press the gas. Claudia We'll do something. You're getting awfully late.  Don't just sit there, David. Tell me what's what the battery's dead The battery what what battery the battery in the car. It's dead Really dead.  This is no time for jokes. I'm not joking. Is this serious? It's exactly what it is. Well, what made it die just burned itself out Me just died without warning us or anything The last time I drove the car. It wasn't even sick. I mean it did not sick Now all of a sudden it's dead. It's dead. All right Well from what somebody must have left the lights burning in the car Now don't look at me like that. I didn't go near the car yesterday. Let alone leave the lights burning if I would Are you sure? Of course, I'm sure. I know when I've been near the car You you drove the car you left at the station and you drove yourself home You put it in the garage. So I never even touched the car yesterday. I guess you didn't attend So I did not kill the battery.  Naughton Now do you take the responsibility? I understand it. I never leave the lights on I put the car in the garage. I remember clearly pushing in the button Here they are now sticking out. Well, just one of those things you do automatically like You know like turning off the gas on the stove. I always forget that when I've done it and then I always remember that I Haven't only you must have really forgotten. Yeah, I guess that's what happened. Well, I forgive you dear Now what will we do now? Let the try to push the car out and let her own down the hill That'll oh David after everything organized so perfectly to think you're going to be late just because you let the battle I don't keep saying that besides it can't be helped Hey, what's this here on the front seat? Oh that oh that's mama's fur coat. Well, what you're doing here? Well, I put it in the car. So you drop it off the furrier in new york. If you don't mind When did you put it in the car? Last night before going to bed. So I'd be sure to remember and not make you late this morning Wasn't that thoughtful of me? Very well, I guess I better start Oh David What's my David when I brought the fur coat out to the car I Well, you see it was already dark. So I Yes, I did. Oh David. No, I couldn't help. I simply couldn't go on going going David darling dearest after all my planning on the one morning when I had everything planned so beautifully Do you think I could have done it? Yes, I think I think you could have done it In factories and offices in big towns and small coca-cola coolers make it possible for people to work refreshed You too can work refreshed at home by keeping plenty of coke in your refrigerator Bring home a case of coca-cola today Then there'll always be a cold bottle ready to refresh you. Hey, Joe How about coming up to the garage and give me a hand with the car? All right, David in a minute It is cold this morning. Winter is really setting in isn't it though? All right, there are a few things I want to do about it tomorrow. Remind me, will you Joe? I will David I'll be with you to help you with the car just as soon as I say that Every day Monday through Friday. Claudia comes to you transcribed with the best wishes of your friendly neighbor who bottles coca-cola So listen again tomorrow at the same time And now this is joking saying au revoir And remember whoever you are whatever you do wherever you may be When you think of refreshment think of coca-cola For coca-cola makes any pause the pause that refreshes And ice cold coca-cola is everywhere This broadcast of claudia was supervised and directed by william brown maloney And now here's a word from your friendly neighbor who bottles coca-cola


Okay, welcome back everyone. This is theCUBE, our flagship program. We go out to the events, extract the signal from the noise. I'm John Furrier, the founder of SiliconANGLE, I'm joined by my co-host, Paul Gillam, with SiliconANGLE, my co-host. And we're here live at IBM Impact, and our next guest is the Baylaw GM of the Power Systems Group at IBM, CUBE alum that we spoke with him just a few weeks ago at IBM Pulse. A lot's changed. Well first, welcome back. It's great to be back in Vegas. It feels like many times already this year. Lots changed. At Pulse, we were talking a lot about some of the power systems and kind of how that HPC, mainframe, all that software enablement, but a lot's changed. Big announcements to everyone. Cisco, just give us an update quickly. What's transpired since Pulse to today? Yeah, so thanks John. Thanks John and Paul for having me here today. As you said, a lot has changed. We've been moving very fast with our power platform to connect it to the whole trends we see in the marketplace around cloud analytics, mobile and social. At the end of the day, it's really around data. And what we see from the new power-each systems is they are squarely designed to focus on solving the big data problem. So as these new systems come to market, they're not just addressing the traditional sort of relational database structure data. They're working on solving client problems around just scale of data, but all kinds of data. Unstructured, mobile data, right? MongoDB, right? No SQL, the list goes on and on. So data is a big trend. The other is economics for the cloud. These are really our first systems designed for scale out computing. Driving a differentiated price point for the cloud. And the third is the whole aspect around openness. We have fundamentally opened up the power platform. Paul and I were talking in the intro, IBM's obviously 50 years of innovation to the mainframe celebrating. That's kind of like Apple Pie and hot dogs and baseball. You know, it's great, but it's not a strategic, it's a cash cow, but it's not a strategic thing. But we were talking in Paul's just moved to the cloud. And in that sense, it's like a mainframe concept. So share with the folks out there that the tea leaves, read the tea leaves around, okay, mainframe's great, great legacy, you know, the motherhood of the mainframe's great, but now it's moving to cloud. What similarities are you seeing from those mainframe growth days where it was a real force and how is cloud becoming that new, in my words, the new kind of mainframe for lack of a better description? And how does that software component play into it? Yeah, certainly from a cloud standpoint, what we see is clients with on-premise infrastructure looking to find ways to rapidly and flexibly sort of move to a hybrid infrastructure. Yeah, so perhaps the cloud is a place they do their mobile application, they compose the objects together, they do their web enterprise applications, quickly connecting to that backend infrastructure. We saw some great examples of that here in Marie's section just moments ago on stage. So this hybrid notion, I think is really where we'll see enterprises going, leveraging their power infrastructure or mainframe infrastructure on-premise and connecting that to the cloud. Could be the IBM cloud or some other cloud. In the IBM cloud case, it could be running power here with our announcement at Pulse of power as part of the software infrastructure. One of the things you've done, Doug, is you created the Open Power Foundation now really to re-emphasize the idea that power is an open platform and you're looking to bring other partners into the fold. How are you, what are you doing to convince companies who may be accustomed to thinking of IBM as proprietary, as all or nothing to have a platform that you really are open, you really do want to involve them? Well, one of the interesting trends we see, sort of as we deal with this sort of composable application, composable enterprise model is every company is looking for the best technology to solve the issues they have. But the best technology doesn't necessarily mean it comes from one company. And they're all incredibly uncomfortable with one company setting the innovation agenda. So with our Open Power Foundation, we've said, you know what, we completely agree. IBM cannot be the company that thinks we can do it all. It's going to take a community of innovators to bring together the best pieces to solve different problems. So that started with an idea with Google, NVIDIA, Melanox, and TyAnne, the founding five members. It now has blossomed up to 26 members and growing daily. In fact, in San Francisco last week, we were signing new partners such as Canonical, which brings a bun through the market, and Rice University, who's working with the Texas Medical Center into the Open Power Foundation all around innovation and solving real problems with new approaches. And nevertheless, when you look at the members of the foundation, there's one company that stands out and that is Google. I thought you were going to say IBM. How important is Google's endorsement and they're really taking this ball and running with it to the success of this initiative. Yeah, so Gordon McKean is from Google. He's responsible for their infrastructure. He's also the chairman of the Open Power Foundation. So they've had a very strong hand in setting the direction for where the Open Power Foundation goes so far. And obviously, with Gordon as the chairman, he will continue to do that. They play a strong role in not only what they're going to do with it, and I mean, they've contributed developers, they've contributed software to the Open Power Foundation. Obviously, we've contributed the Powerade architecture in a licensing model, but also reference design. So, and I think that's what's exciting people to join. If you look at the memory companies joining the accelerator companies joining, and now really the new trend is end users joining. And I think that's creating sort of this whole global movement around open this versus closed. What does an end user have to gain by joining a hardware design coalition? Yeah, and we actually see it not as a hardware, although that's certainly where it started, Paul. So I acknowledge that. It's really sort of this end to end ecosystem around innovation. What I see end users looking for, back to this point of flexibility, speed of development, rapid, composable, fit my need is what they're seeing, fit my need. I don't want to feel like somebody else is defining what I need. I want to be able to take the best pieces and fit them together. Some of great examples would be the ability to use Powerade systems with NVIDIA, right? And bringing that sort of hybrid compute model of NVIDIA for GPU acceleration, say for Java workloads, great example of 10x acceleration with Java workloads with NVIDIA plus Powerade. We've got another example down on the floor of, again, composing together these systems to go do Monte Carlo simulation for the finance market. What is a magnitude improvement in performance? So we're seeing, we've got some great demos down on the floor of these sort of, couldn't you imagine? What if you could put together these pieces in a composable system and bring that to new use cases? I've got some questions out in the Twitter sphere in the social crowd chat. If you're watching this, you want to ask Doug a question, go to crowdchat.net slash IBM impact. We'll be fielding questions there. We've got the first question coming in. IBM Power sounds so IBM centric. How is IBM changing that perception to be broader? And how are you tracking non-IBM customers to come along with this new offering? Well, certainly Power is the IBM brand for our core processor, the Powerade processor, but then the systems we build on top of it. One of the aspects of Open Power is there will be other server companies in the market who will bring this power technology to their clients. So as I think about Open Power, I sort of describe it this way. It is about bringing power technology to new buyers and new markets, new buyers potentially being clients like Google and others in the sort of the hyperscale data center, and new markets like China. Certainly China is undergoing a tremendous change in the way in which they think about the domestic IT market. It's also about creating this innovation pipeline so that this community of innovators who are coming up with creative ideas to solve different problems I've described are able then to sort of bring this innovation to the power platform. So we're absolutely opening it up and I think of no better way to attract new buyers than to talk about openness. And certainly Google will be here. Google's involved in the openness of this. Talk about Google's role involved in power. Yeah, I can't, obviously I can't talk for Google. That's only Google for Google. No, that wouldn't be appropriate for me. I can't talk about the role, as I mentioned a minute ago, in terms of a chairman of the Open Power Foundation. I do understand here, down on the demo floor, Google has brought their own Powerade motherboard and I think Gordon McKean will be showing that off down there if anybody wants to stop by and see it. You announced a pulse that you'd be moving power to SoftLayer and lots of Watson on top of SoftLayer by the autumn, by the fall. Is that schedule still on track? Actually, if you saw a minute ago, what Mike wrote and was talking about in terms of Watson available in the cloud, that's actually running on Power this quarter. Is that for developers only at this point for business partners or is that for end customers as well? I think if I remember from what Mike described, it's really across the spectrum of potential users, developers and users as well. It's a great question for Mike, sort of the ultimate consumption of it is in his space. But from a rollout for Power in the SoftLayer, now it's interesting, we've sort of been talking about these things you mentioned, Paulson, obviously over the last couple of quarters and months. Underneath it all has been Powerade, we just never said that. When we talked about our commitment to KVN and Linux, the little Indian Linux, by the way, for ease of application porting, it was all about Powerade. When we talked about Watson as a service, it was about Powerade. We talked about Watson and SoftLayer, Powerade. We're sort of now here, so we've been sort of building up to this over the last nine months. So I want to ask you, Doug, one of the things that comes off, see IBM is so good about the messaging. You guys are all, you're right on the fault line of all the killer megatrends as the place shift and the tectonic shifts in the industry. One of them is real-time analytics. The other one that we were talking on the intro is this whole trend towards this maker movement. And I was commenting, I was at the Macintosh's 30th anniversary celebration of the Mac, and then, you know, and the open compute was now on this the next week. This movement towards tinkering and hacking on hardware with open source software really put a big trend. So you're seeing some things with Raspberry Pi here. Developers are really geeking out on this maker movement. It's really spurring creativity. So I got to ask you, how does that power, you hit a nerve there with power. So how is a developer who really wants to get their hands dirty and build software, how does the power system help them? What kinds of things can they do? Is it analytics, is there more sexier applications? What's your take, share some color on that? Yeah, so as we think about the sort of where power plays best in the marketplace. Certainly, from a design point, we see power really, as I said earlier, addressing all the types of data. And the good news is, there's no lack of data right now, right, and it's all kind of different kind of data that we see going on in the marketplace. So, you know, we talked about as an example, IBM Cloud, clouded a no SQL database for SaaS. So think about the benefits one could see of no SQL data on power and software, which is something we're actually working on, right, from moving power into that sort of no SQL space. So I think any aspect around data is a good fit for the power architecture. Now to your tinkerer question, one of the things we've really focused on here with this launch is making application and tinkering simple on power. And we've done that by completely supporting an open stack of software from Linux, not big Indian Linux, if you want to get a little geeky for a second, it's really the little Indian. What does that mean? It's the bitmaps are the same way as they are on x86. So now with little Indian Linux, KBM as a hypervisor, open stack for management and then the smart cloud portfolio on top, you've got a completely open stack of software that makes picking up a higher level language application, you can pick it up and drop it over on power without a single change to it. Think about minutes versus hours or days of what it used to take. The same is true of CC++. It's a simple recompile and go for 95% of the app. So we truly have addressed this sort of speed and development of applications on power. Doug, IBM sold off its x86 business to Lenovo and now you set up the OpenPower Foundation. Are you directly in conflict with Intel at this point? Are you competing directly with Intel? I think for the targeted workloads, I'm talking about data-centric workloads, enterprise applications based on Java, workloads such as mobile that are enablement to the core, absolutely yes. In fact, the economic point I made earlier, we see the economics of our scale off platform which delivers great performance at up to 20 to 30% less acquisition price. So it's a direct play for the infrastructure market. How important is it to you? You currently don't have any partners who are actually fabbing the PowerAge chips. How important is it to you to get a partner in the door actually making PowerAge? Yeah, the fab part isn't the most important part. What's important to me from an ecosystem is having chip development companies with me that are doing derivatives of the power architecture like Suzo PowerCore. It's about having IO members, memory members, software partners doing software around it and around end users. Building out that ecosystem now at 26, as I mentioned in growing, is really the focus of the open power foundation. If somebody wants to join from a fab, we're completely open to that, but I don't think that's as super important as the other areas. There have been previous efforts by companies to create sort of standards around risk architectures, PA risk, sun risk, even IBM many years ago. What did you learn from those efforts, most of which didn't go very far. What did you learn from those efforts that you're applying to power foundation? Yeah, I mean it always starts with, and it's going to sound kind of weak, but it always starts with listening to the marketplace. And the big thing that we did this time, and I would give Google credit for us for grabbing us by the shoulders virtually and saying, guys, get on with the Linux play. Get on with it in a big way and make it a little Indian so it's easy for applications to port to. And Buntu, we'll talk later here today with me about the way in which they've taken thousands of applications now within their ecosystem and brought them to the power architecture. They couldn't have done that before. So that was sort of the big aha moment we had based on the open power relationships. This get on with it from a Linux client, so the market's chosen around an open stack of software for new application development. You've mentioned to Buntu a couple of times now, are they sort of the preferred Linux platform for power? No, I would say they're the most recent to join. We continue to have great relationship to Red Hat and Suse. And Buntu happens to be the new one we're announcing today, is sort of the third member of the distro. There also happened to be the first bringing little Indian Linux to the platform. The others have plans in the future, but that's partly why I mentioned them. They're new, and then the first with little Indian Linux.  That's right. You were trying to tell a Linux story to those, to that group of course, ZOS focused very much a different kind of migration play there. What did that experience teach you as you're trying to promote Linux as really the platform going forward for the future? Yeah, I mean Linux on the mainframe has been incredibly successful. If you look at the capacity now we ship each quarter on the mainframe, the majority of that capacity is now for Linux applications on the mainframe versus sort of that core infrastructure that's existed for years. So it has been a great enabler for new application capture on the mainframe. What did I learn? Get on with it. Back to the point of the application developers have decided OpenStack of Software is the right answer. So me trying to convince them to do new application development on my core infrastructure of AX and IBMI, it's a much harder play. That remains super important though. And this is the question just like the mainframe I get all the time. AX, IBMI, super important to my strategy going forward. It's where my tens of thousands of clients are today. I need to augment that though with a new application capture engine and that's Linux. That's what I learned. Talk about the investment you're making in the power. Obviously IBM is all in on Linux. You see OpenStack big part of the blue mix, all the cloud stuff, blue acceleration, a lot of stuff in the portfolio. So talk about how this fits in with the existing portfolio within IBM. And also how does this tie into some of the key applications around analytics and then the cloud. What is it? I mean, are you guys not giving up the hardware per se?  You're seeing that being more of an enabling strategy with openness. So how does that all reconcile? I mean, you got big dollars going into the market with Linux. Take us through that next generation roadmap. Where does it lead to? Yeah, great question.  In fact, the power aid processor, really what we see as the first processor design for big data, that started over three years ago. And we saw the problem coming in the market of a true need for a system and processor that was going to help clients with the big data problem. We've spent, I think, our best estimate is over two and a half billion dollars in those three years developing power aid processors and the technology around it. So pretty significant investment. Recently, as you mentioned, John, we announced our second billion dollar commitment to Linux. This time, Linux on power. And it's really about the ecosystem. It's about the porting centers. It's about the IS fees. It's about the go-to-market and obviously the products as well too. So- I mean, a billion dollars is not that much money these days. How about 10 billion?  Ah, come on. I think we'd all agree. I'd take a billion anyway, right? A billion is still an important number, right? For a company the size of IBM as well. So sizable investments we've made. Now to your point earlier in terms of, so where is this play out? You know, we're not getting out of the power of hardware business. This is incredibly important. Our chairman, Ginny Romendi, has been very clear on the importance of, you know, what we call high-end, high-value systems and the role power plays in that. I actually think with the divestiture that's still underway, this helps sort of get clarity of the portfolio where we're placing our bets from the server. We need to be more specific. And where we can bring value and innovation. Yeah, I mean, you guys have a lot of value. I mean, if you pick a customer base vertically, you guys are pretty much there, but I want to get more specific around HPC because HPC market's changing, right? It used to be throw a box at it and you're done. Right, right. Now you got cloud as a big part of the HPC equation. You're talking about compute, a lot of unlimited compute theoretically, but big data is kind of the things where we're going to talk about internet of things today. Right. There's all kinds of stuff going on in the cloud. So it's not so much the big data pipe, it's the pilot data. So if someone wants to do a computation, is this kind of where you see it going? Is that the focus? Is it the, is HPC the new, is HPC, what is the new HPC? Yeah, so I say the new HPC is much more analytics driven than it is pure compute, right? If you think about the scenes, the scene HPC was all just about compute part, right? To be able to run fast, that's still important, but what we see, and to no surprise again, is many of these, whether it be government oriented, utilities, whatever it happens to be, are very much focused on the same problem commercial clients are, data. And so HPC evolves to, sometimes we call it HPA, high performance analytics, taking advantage of this, lots of cores, lots of threads, large memory working space, and yet very big IO bandwidth to move the data around. So I got to ask Paul, because we're a throwback here. It's not throwback Thursday yet, but are we going back to MIS departments and data processing departments? I mean, you're basically talking about data processing. This is data scientists, right? I mean, we see kind of this role evolving around folks who sort of focus every day on the science of data, getting business value out of this gobs of data they have. You've got a lot of partners working with the PowerAid reference spec right now. Can you give us an idea preview when we might see chips coming out that would include, say, an IBM Power with NVIDIA or Melanox? You know, I can obviously, again, speak for them and announce their own plans. What would you like to see? You know, I think the faster we create innovation, the better for the marketplace. I know one thing that is being shown down on the floor and was publicly stated by NVIDIA last week, so I'll repeat it, is this sort of marriage between NVIDIA GPUs and Power on a single system. I think you can look for that later this year. We got some commentary from the crowd again. Tim Crawford, shout out to Tim. My point of view, IBM would do well to play down their hardware position, not build on it. IBM's hardware play is better suited for cloud providers than enterprises moving forward. What's your comment on that, on his take on that? Yeah, I think part of it is, so we're not going to play it down, obviously we're loud and proud, right? So I'm putting that part aside for a second. I do agree with them on the role the cloud plays. You know, I think what we see going forward is this incredibly important role around sort of what we call sort of the hyperscale clients. Those are building out the Internet data center that we talk about at sort of the dinner table and at home every day. But then there's the managed service providers, those who are sort of much more mid-sized and have drawn a circle on a map and said, you know what, I'm going to be the service provider for this city, this state, this country, and we're bringing power technology to them, sort of married with PureFlex, by the way, for the mid-range service provider. And that's got to come with a different economic model by the way in which they acquire that infrastructure. So I completely agree with the second part, power for the cloud is a very important play for us. So in the last minute I want to just get you to take on what you're expecting over the next year, obviously the customer activity here, give us some taste of the meat on the bone with customers and some deployments. Where is the action happening and what do you see projecting out of the next 12 months? Just kind of a high-level execution. Yeah, certainly we are looking to power each systems to be a catalyst for improving our business performance around the power platform. Our CFO, Martin Schroder, has been very clear on as I have been that powering and all we've done to reposition the platform, new applications with Linux, the target for the cloud and the role power plays for big data are where the market's going or gone and is where power's going. So I think from a business perspective we are now very much aligned with the market and based on that we will look forward to strong success and adoption. So next year or next event at Pulse are here. What's the big success, top three things you want to check off to have a good year for power? What's the big objectives? Yeah, I think with anything where you're sort of shifting to a new space for ourselves, although a space that's large, I'm absolutely looking forward to sharing sort of proof points and references around the role power is playing for big data solutions to clients, right? Second part would be the success of open power, continuing to grow, but also a bit more than just growth of members, continuing to bring innovation to the market and continuing to demonstrate as we are today on the show for true innovation that benefits clients in the end. As people start to instrument the business, this is my last question and we'll break and then I'll let you get the last word in, but as customers start instrumenting their business, big data, obviously a big part of it. Yes. Now you're starting to see the convergence of physical spaces, the work environment. It could be in the hospital, machines, to other physical attributes. How do you see that vision of the internet of things playing out with regard to power? Yeah, I think it comes back to, clients want to consume IT in the way in which they want to consume it. It could be infrastructure as a service, it could be platform as a service, it could be software as a service. My goal is to bring power to however they want to consume it, right? It could be on-premise, it could be on-premise in the cloud, it could be as a way in which we deliver phenomenal benefits under a blue mix composable set of applications. So however they want to consume IT, power will be there. Does that include embeddable devices? You know, less focused on embeddable. I mean, we've had power in the past focused on embeddable. I'm really focused with power and open power on the server market. Sometimes that server is more of an appliance based. That's fine, but try putting in the cars and so forth, that's not our focus. Doug, I'll let you get the final word in. Tell the folks out there why this show is so important. What is the main message to your customers and IBM across the portfolio? Yeah, so I think the reason we're at this show announcing the new power systems is back to the point of the changes we see in the marketplace. This, every mobile transaction, right? Every reach to the cloud, every social post, it drives data. And data ultimately does depend on the infrastructure. And the infrastructure we believe certainly matters. That's why we're investing in new power systems focused on, back to what I said before, data, cloud and being the most open server platform in the marketplace. Doug, the general manager of the power systems group at IBM. I mean, I'm the main creator of 50th anniversary. Like I was saying earlier, data processing is back in vogue the whole term. But that's what's happening. It's data science, data processing. This is theCUBE. We're processing the data and sharing it with you. We'll be right back with our next guest after this short break.


We've been learning how to differentiate all semester, now we want to go backwards. So let's throw down a definition of an anti-derivative. Suppose the derivative of capital F is equal to lowercase f of x. Then capital F of x is called an anti-derivative of f of x, and we use the notation squiggle f of x dx equals capital F of x, where the squiggle is our symbol for anti-derivative. We say that f of x is the integrand, and dx is the differential. And here's a very, very, very, very, very, very, very, very important idea to keep in mind. The differential variable should be the only variable in the integrand. If there are other variables in the integrand, we can't proceed, at least not until we take calculus 3. So for example, we want to show that cosine squared x plus 5 is an anti-derivative of minus 2 cosine x sine of x, and then find two other anti-derivatives. So we'll pull in our definition of anti-derivative. It's an anti-derivative if the derivative is what our function is. So the easiest way to verify this is to differentiate. Is it true that the derivative of cosine squared of x plus 5 is 2 cosine x sine of x? Well, let's check it out. So I want to find the derivative of cosine squared of x plus 5. And since this is a sum, we know the derivative of a sum is the sum of the derivatives. Now, remember that cosine squared of x is shorthand for cosine of x squared. And so this function is a squared function. It is a something squared. And the derivative will be 2 something to the first times derivative of our something. Meanwhile, here we want to find the derivative of 5, which will be 0. And we have an unresolved derivative here, derivative of cosine x. And the derivative of cosine x will be minus sine of x. And so our derivative will be minus 2 cosine x sine of x, which is what we want it to be. How can we find other anti-derivatives? The important thing to recognize is that in our derivative, we took the derivative of a constant, which was 0. And that's going to be true for any constant at all. And so changing the added constant won't change the derivative. So instead of cosine squared of x plus 5, we could have cosine squared of x plus 10, or we can show off and say cosine squared of x plus this horrible mess. And each and every one of these has a derivative equal to minus 2 cosine x sine x. And this leads to the following theorem. Suppose f is an anti-derivative. Then f of x plus c, where c is any constant at all, is also going to be an anti-derivative. How do we find anti-derivatives? So suppose I want to find the anti-derivative of 5x cubed dx. What this means is we want to find a function whose derivative is 5x cubed. And before we proceed, one important check to make. Our differential variable is x, and our function only has variable x in it. And so it's possible to proceed from this point in a meaningful way. But how? We'll fall back on a time-honored strategy in mathematics and in life. We can proceed by guess and fix. We'll guess an answer, and if it's correct, great. If not, we can fix the answer so that it'll be at least more correct. Remember, you don't have to be right at first, as long as you're right at last. So what we want is something whose derivative will give us 5x cubed. And it's helpful to remember a couple of basic derivative rules. The derivative of a constant produces zero. The derivative of a sum produces a sum of derivatives. And the derivative of a constant multiple of a function produces a constant multiple of a function. And this last rule is fairly important, because it means that we can ignore the constant, at least until the very end of the problem. So let's focus on this x cubed. What sort of thing do we differentiate to get an x cubed? Well, one of the very first derivatives we found is that if I have a function x to the n, then the derivative will be nx to the power n minus 1. And so that means if I find the antiderivative, I can increase the power. So this x to the third might have come from the derivative of x to the fourth. Well, let's drop that in and see what happens. If my original function was x to the fourth, then the derivative will be 4x to the third, which is exactly the same as what I want. Oh wait, no, it's not actually exactly the same as what I want. So let's fix it. I don't want a 4 here, I want a 5 there. So let's multiply by 1 fourth, that'll take care of the 4, and then multiply by 5, which we'll put in the 5. And because these are constants, I can multiply them together. And because they are constants, I can move them into the differentiation. And it's useful to remember one more important thing. Once I find an antiderivative, then I can form other antiderivatives by adding any constant at all. And so the antiderivative isn't just 5 fourth x to the fourth, but it's actually 5 fourth x to the fourth, plus any constant that you want. Let's try another antiderivative. So we want to find a function whose derivative is e to the 3x. So we might ask ourselves, self, what produces something that looks like e to the 3x? And we might remember the world's easiest derivative. The derivative of e to the x is e to the x. And so maybe this e to the 3x came from e to the 3x. Well, let's check it out. If I differentiate e to the 3x, then I get e to the 3x times 3, because we have to use the chain rule. And it's not quite what we want, but that's okay. We can fix it by multiplying by 1 third. And again, any added constant won't change the derivative. So our antiderivative looks like it's going to be 1 third e to the 3x plus c. That was fun. How about another antiderivative? As usual, it's helpful to identify what type of function we're dealing with here. In this case, our integrand is a sum, and we know that the derivative of a sum is the sum of the derivatives. So this 5x cubed plus e to the 3x must have come from a sum of derivatives. So we need to find something whose derivative is 5x cubed, which we already did, and we need to find something whose derivative is e to the 3x, which we already did. Now, note that we didn't include the constants. What we can do is we can lump all of those constants together into a single constant right here at the beginning. All right, let's look at another antiderivative. This is a product. And unfortunately, none of our derivative rules give us a product. Remember, even the product rule gives us a sum. So we should try something else. We could always try some algebra. This is a product, and we can multiply out. And so instead of trying to find the antiderivative of a product, which we have no rules to handle, we can instead try to find the antiderivative of 6x squared minus 13x minus 5. So we'll invoke gas and fix. We want to find something whose derivative is 6x squared. So again, I'm guessing this is going to come from something like x to the third, except when I differentiate x to the third, I get 3x squared, which isn't what I want. But if I multiply it by 2, I will get what I want. And that factor of 2 becomes part of the antiderivative. I also want to get a 13x. That's 13x to the first. And so that probably came from something like x squared. But when I differentiate x squared, I get 2x. So I need to fix it. And I can include that factor of 13 halves as part of the antiderivative. And then finally, I want that antiderivative of 5. And so that must have come from something like 5x. So I can put the pieces of the antiderivative together and don't forget, plus any constant at all.


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