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 $0$.