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Subdifferentiation at a point

  1. Mar 15, 2008 #1
    Define f:R->R by
    f(x) = { x^2 sin(1/x) x!=0, 0 x=0
    Compute subdifferential f(0)

    I went through my notes on subdifferentiation and still do not have a clue how to do this process, is there a formula to directly do this? any help would be greatly appreciated.
  2. jcsd
  3. Mar 16, 2008 #2

    Gib Z

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    On the entire of the world wide web, the first result on "subdifferentiation" comes from this thread. What exactly is subdifferentiation?
  4. Mar 16, 2008 #3


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    Wikipedia says: http://en.wikipedia.org/wiki/Subderivative

    (I know what people are going to say; don't link to wiki; but there doesn't really seem to be another website on this this is openly accessible!)
  5. Mar 16, 2008 #4

    Gib Z

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    Ok with that definition:

    What makes you (the OP) think that we can find the subderiavative at zero? Is the function convex...
  6. Mar 16, 2008 #5
    the function is not convex. but it is an assignment question so it must be doable some how.
    so i looked at the wiki you sent me and saw the example. but then i guess it is not the same
    as my question as that function is convex and mine is not.
    Example i am referring to:
    Consider the function f(x)=|x| which is convex. Then, the subdifferential at the origin is the interval [−1, 1].

    But with that said, I graphed the x^2sin(1/x) function to try to see the behaviour around 0, and both sides are approaching 0 and the slope seems to be also 0.. but i don't know if this is how to actually do it.

    what are your thoughts after that wiki read?

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