to prove that a function is a Differentiable function?

Asked Mar 06 '15 at 01:19

Active Mar 06 '15 at 01:19

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let $f:\mathbb{R} \rightarrow\mathbb{R}$ be a continuous function in $x_0\in\mathbb{R}$.

In addition, $f'(x)$ is defined for every $x\in(x_0-\delta,x_0+\delta),x_0\notin(x_0-\delta,x_0+\delta)$

In addition, i know that $\underset{x_0}{lim} f'(x)=L$

how can i prove that $f(x)$ Differentiable in $x_0$ ?

at first, i thought that we can use the Mean value theorem,but i'm not sure if the conditions are sufficient.

asked Mar 06 '15 at 01:19

Amit

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There seems to be some typo there. Surely you can't have $x_0\not\in (x_0-\delta;x_0+\delta)$. – user26486 Mar 06 '15 at 01:22
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It seems to me that when the question is fixed this will be a duplicate. – Git Gud Mar 06 '15 at 01:29
hi Git, is i saw the answer there, is it ok to use the Mean value theorem also in my case? as stated in your link? – Amit Mar 06 '15 at 09:09
@Amit Yes.${{}}$ – Git Gud Mar 06 '15 at 09:41
thank you very much. case closed. – Amit Mar 06 '15 at 09:54

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