Mean value theorem

Let $a<b$ be real numbers, and let $g:[a,b]\to \mathbb{R}$ be a function continuous on $[a,b]$ differentiable on $(a,b)$. Then, there exists an $x\in (a,b)$ such that: $$g^{\prime }(x)=\frac{g(b)-g(a)}{b-a}$$