This worksheet illlustrates Rolle's Theorem applied to the function [math]f(x) = x^5-5x+2[/math].

[list=1] [*] Adjust the point labelled [color=#0000ff][math]a[/math][/color]. The points labelled [color=#6600cc][math]b[/math][/color] indicate the values of [math]x[/math] for which [math]f(x) = f(a)[/math] as required by Rolle's Theorem. [*] The points labelled [color=#ff0000][math]c[/math][/color] are the values of [math]x[/math] in the intervals [math](a,b)[/math] for which [math]f'(x) = 0[/math]. [*] See what happens when [color=#0000ff][math]a[/math][/color] moves further to the left or the right. [/list]