Let $f$ be a real valued continuous function on $[ 0,2 ]$ which is differentiable at every point except possibly at $x = 1$. Suppose that $\lim _ { x \rightarrow 1 } f ^ { \prime } ( x ) = 2013$. Show that $f$ is differentiable at $x = 1$.
Let $f$ be a real valued continuous function on $[ 0,2 ]$ which is differentiable at every point except possibly at $x = 1$. Suppose that $\lim _ { x \rightarrow 1 } f ^ { \prime } ( x ) = 2013$. Show that $f$ is differentiable at $x = 1$.