Rolle's Theorem

analysis

Definition

Rolle's Theorem

Let $f$ be a continuous function on $[a,b]$ and differentiable function on $(a,b)$. Furthermore, $f(a)=f(b)(⟺f(a)-f(b)=0)$. Thus, there exists a $\xi \in (a,b)$ with $f^{\prime }(\xi )=0$ according to the mean value theorem.