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Homework Help: Fundamental Theorem of Calculus properties

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data

    Find a function f : [-1,1] ---> R such that f satisfies the following properties:

    a) f is continuous
    b) f is restricted to (-1,1) is differentiable
    c) its derivative f' is not differentiable on (-1,1)

    2. Relevant equations

    3. The attempt at a solution
    I kinda think that the mean value theorem and Theorem 2 of the fundamentals [tex]\int[/tex]f(x)dx = F(b)-F(a) got some link but I can't seem to get it. I do understand that for f'' not to exist, x should be undefined on the (-1,1). Please help.
  2. jcsd
  3. Apr 2, 2009 #2
    A read somewhere that a hint would be to begin with an absolute value and use [tex]\int[/tex]f(x)dx = F(b)-F(a) (fundamental theorem of calc prep 2) repeatedly.. but still puzzled
  4. Apr 2, 2009 #3


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    Homework Helper

    Start with c). Pick a nondifferentiable function on (-1,1) and integrate it to get f.
  5. Apr 3, 2009 #4


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    |x| is a very simple function that is not differentiable at x= 0.
  6. Apr 3, 2009 #5
    You are right, but the OP is looking for a function such that it is once differentiable on (-1,1) but not twice, and is continuous of course on the same interval.

    Edit: ignore it!
  7. Apr 3, 2009 #6


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    Yes, and combining |x| with Dick's suggestion gives exactly that!

    (Edit: Too late! I gotcha!)
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