# Thread: prove that f is derivable.

1. ## prove that f is derivable.

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.

2. 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

3. May be is to prove if the function f is differentinable everywhere in R or not?

4. ## mande fruta sorry for my bad english

Yes prove if the function f is differentiable in x=0 or not

5. 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