Search Results for “function-input”

Exploring Rolle's Theorem
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?