Q:If $f:[a,b]\to \mathbb{R}$ is continuous on $[a,b]$, differentiable on all $t\in(a,b)\setminus\{x\}$, and $\lim\_{t \to x} f'(t)$ exists, then f is differentiable at $x$ and $f'(x)= \lim\_{t \to x} f'(t)$.

I just need a small hint to keep me going on (no solution please). Thanks