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Math Help - differentiability

  1. #1
    Junior Member
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    differentiability

    Given f: (a,b) -> R is differentiable at p in (a,b)
    1. prove f'(p) = lim n->infinity (n[f(p+1/n)-f(p)])
    I already this this part using the definition of f'(p)

    2. By example, show that the existence of the limit of the sequence {[f(p+1/n)-f(p)]} doesn't imply the existence of f'(p)

    I don't know how to go about this one. Please provide some hints
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  2. #2
    Super Member Failure's Avatar
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    Quote Originally Posted by inthequestofproofs View Post
    Given f: (a,b) -> R is differentiable at p in (a,b)
    1. prove f'(p) = lim n->infinity (n[f(p+1/n)-f(p)])
    I already this this part using the definition of f'(p)

    2. By example, show that the existence of the limit of the sequence {[f(p+1/n)-f(p)]} doesn't imply the existence of f'(p)

    I don't know how to go about this one. Please provide some hints
    Surely, you have already seen examples of functions that are not differentiable. For example, f(x):=|x| is not differentiable at x=0. Or, to shift the whole thing from 0 to p, you can take f(x) := |x-p|.
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