# Rolle’s theorem

Rolle’s theorem. If $f$ is a continuous function on $[a,b]$, such that $f(a)=f(b)$ and differentiable on $(a,b)$ then there exists a point $c\in(a,b)$ such that $f^{\prime}(c)=0$.

Title Rolle’s theorem RollesTheorem 2013-03-22 11:51:26 2013-03-22 11:51:26 drini (3) drini (3) 14 drini (3) Theorem msc 26A06 IntermediateValueTheorem MeanValueTheorem ZeroesOfDerivativeOfComplexPolynomial