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Math Help - prove that f is derivable.

  1. #1
    Member kezman's Avatar
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    prove that f is derivable.

    A difficult problem.


     f:R \longmapsto R
     |f(x)| < x^2
    Prove that f is derivable or find an example of a f(x) not derivable.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by kezman View Post
    A difficult problem.


     f:R \longmapsto R
     |f(x)| < x^2
    Prove that f is derivable or find an example of a f(x) not derivable.
    Do you mean find f(x) which is differentiable nowhere in \mathbb{R}, or at some given point or at 0?

    RonL
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    May be is to prove if the function f is differentinable everywhere in R or not?
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    Member kezman's Avatar
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    mande fruta sorry for my bad english

    Yes prove if the function f is differentiable in x=0 or not
    Last edited by kezman; December 25th 2006 at 01:31 PM.
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by kezman View Post
    Yes prove if the function f is differentiable everywhere in R or not
    Try the function:

    <br />
f(x) = \left\{ {0,\ \ \ x\ \mbox{rational} \atop x^2/2,\ \ \ \mbox{otherwise}}\right.<br />

    Which is differentiable at x=0 but nowhere else.

    RonL
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