Explore conditions of the Rolle's Theorem.
The applet shows the graph of continuous differentiable function f(x) on a closed interval [a, b].
Case 1. f(x) < f(a) for some x inside the interval (a, b).
Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0?
Case 2. f(x) > f(a) for some x inside the interval (a, b).
Can you find the number c such that f'(c)=0? What did you notice about the point when f'(c)=0?
Can a given function have more than one number on a given interval such that f'(c)=0?
Tags: Calclulus
