Real function/Theorem of Rolle/Fact

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

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

be a continuous function, which is differentiable on ${\displaystyle {}]a,b[}$, and such that ${\displaystyle {}f(a)=f(b)}$.