A difficult problem. $\displaystyle f:R \longmapsto R $ $\displaystyle |f(x)| < x^2 $ Prove that f is derivable or find an example of a f(x) not derivable.
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Originally Posted by kezman A difficult problem. $\displaystyle f:R \longmapsto R $ $\displaystyle |f(x)| < x^2 $ Prove that f is derivable or find an example of a f(x) not derivable. Do you mean find $\displaystyle f(x)$ which is differentiable nowhere in $\displaystyle \mathbb{R}$, or at some given point or at $\displaystyle 0$? RonL
May be is to prove if the function f is differentinable everywhere in R or not?
Yes prove if the function f is differentiable in x=0 or not
Last edited by kezman; Dec 25th 2006 at 12:31 PM.
Originally Posted by kezman Yes prove if the function f is differentiable everywhere in R or not Try the function: $\displaystyle f(x) = \left\{ {0,\ \ \ x\ \mbox{rational} \atop x^2/2,\ \ \ \mbox{otherwise}}\right. $ Which is differentiable at $\displaystyle x=0$ but nowhere else. RonL
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