# proving a function is differentiable at a point

Hi guys Im really having problems with this question:

Suppose $g$ is continuous in $(-1,1)$ and differentiable in $(-1,0)\cup(0,1)$. Prove that if $\lim\limits_{x\to C^+}g'(x)=\lim\limits_{x\to C^-}g'(x)$ with both limits finite, then $g$ is differentiable at $0$.

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The image that you supplied seems to have limits as $x\to C^+$ and $x\to C^-$, so that’s the way I edited it, but I’d bet that those should be limits as $x\to 0^+$ and $x\to 0^-$. –  Brian M. Scott Apr 8 '12 at 11:20
Hi mugool. If this is homework, you should put the homework tag. –  yohBS Apr 8 '12 at 11:31
Please tell us what have you tried. Also, consider Brian's remark there--Brian should be right or the problem does not make much sense. –  user21436 Apr 8 '12 at 17:59