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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 $x\to 0^-$.2012-04-08
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    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.2012-04-08

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