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Math Help - Prove that Lipshitz function is differentiable

  1. #1
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    Prove that Lipshitz function is differentiable

    Let f: \Re \mapsto \Re satisfy a Lipshitz condition of order p. Is f differentiable everywhere when p>1 and p=1?

    a) p > 1

    b) p = 1; Let x,y \in \Re \ , \ |f(x)-f(y)| \leq C|x-y|^{p}, then we have  \frac { |f(x)-f(y)| } {|x-y|} \leq C \ \ \ \ \ \ C > 0

    I tend to think that f is differentiable when p=1, but not p > 1, but I'm stuck on actually proving it here.

    Thank you.
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  2. #2
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    No it is not true let f(x)=|x|.
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