Proof of Mean Value Theorem (and Rolle's Theorem)
Instructions
Use this dynamic activity to explore the proof of Mean Value Theorem (and Rolle's Theorem). Drag the point f(c) to make the corresponding point f'(c) meet the pink line of . Construct function d(x) as shown in the activity and verify d(a)=d(b), then apply Rolle's Theorem.
Reflection Questions
1. what is the relation between the slope of f'(x) at point c and the slope of the secant line ()? 2. For the point when f'(c)= , observe the corresponding point of d(x), what is so special of that point? What is the derivative d'(x) of that point? 3. How to write the proof from the demonstration of this activity?