An Overview of Rolle’s Theorem

A detailed tutorial on how to solve problems using Rolle’s Theorem. Step by step tutorial including examples of how to solve problems using Rolle’s Theorem for reference.

Rolle’s Theorem is a special instance of the Mean Value Theorem, and can be used to prove the Mean Value Theorem. Rolle’s Theorem states that a differentiable and continuous function, which attains equal values at two points, must have a point somewhere between them where the slope of the tangent line to the graph of the function is zero. Mathematically this can be expressed as if a real-valued function f is continuous on a closed interval [a, b], differentiable on the open interval (a, b), and f(a) = f(b), then there exists a c in the open interval (a, b) such that f ‘(c) = 0.