Here we illustrate [b]Rolle's Theorem:[/b] If a function [math]f[/math] satisfies the three conditions[br][list][*][math]f[/math] is continuous over the closed interval [math][a,b][/math], [/*][*][math]f[/math] is differentiable over the open interval [math](a,b)[/math], and[br][/*][*][math]f\left(a\right)=f\left(b\right)[/math],[/*][/list]then there exists at least one number [math]c[/math] in [math](a,b)[/math] for which [math]f'\left(c\right)=0[/math]. [br][br]Drag the [color=#980000][b]brown point[/b][/color] to see a geometric illustration of Rolle's Theorem.

[i]Developed for use with Thomas' Calculus, published by Pearson.[/i]