Question

State Rolle's theorem.

Answer 1

Rolle's Theorem:

Let f be a real valued function defined on the closed interval $\left[a,b\right]$ such that
(i) it is continuous on the closed interval ​$\left[a,b\right]$,
(ii) it is differentiable on the open interval $\left(a,b\right),$ and
(iii) $f\left(a\right)=f\left(b\right)$
Then, there exists a real number $c\in \left(a,b\right)$ such that $f\text{'}\left(c\right)=0$.