Rolle’s Theorem

Rolle’s theorem is a special case of the more general mean value theorem.

It says that if you have a real valued function which is continuous over the closed interval [a,b] and is differentiable over the open interval (a,b) and which takes the same value at the two end points, i.e. f(a)=f(b), then there will exist a point c between a and b where the derivative of the function is zero.

In this video we first explain the theorem and then prove it from the abstract analytical definitions.