# Search Results for “Theorem” ##### 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?

Tags: Calclulus ##### Application of The Mean Value Theorem to problem solving
If f(2) = -2 and f'(x) >=2 for 2<=x<=6, how small can f(6) possibly be?

Tags: calculus ##### Application of The Mean Value Theorem to problem solving
Prove |sin a – sin b|

Tags: calculus ##### Application of The Mean Value Theorem to problem solving
Given function f(x) = arctan (1-x) on the interval [0, 1].

Tags: calculus  