Differentiable functions/Mean value theorem/Fact

Let ${\displaystyle {}a<b}$, and let

${\displaystyle f\colon [a,b]\longrightarrow \mathbb {R} }$

be a continuous function which is differentiable on ${\displaystyle {}]a,b[}$.

Then there exists some ${\displaystyle {}c\in {]a,b[}}$, such that

${\displaystyle {}f'(c)={\frac {f(b)-f(a)}{b-a}}\,.}$