Proof of Generalized Mean Value Theorem
Instructions
Use this dynamic activity to explore the proof of Generalized Mean Value Theorem. Drag point c and let the point of [f(b)-f(a)]g'(c) meet with the point of [g(b)-g(a)]f'(c). Construct function h(x) as shown in the activity and verify h(a)=h(b).
Reflection Questions
1. For the point when [f(b)-f(a)]g'(c)=[g(b)-g(a)]f'(c), observe the corresponding point of h(x), what is so special about that point? What is the derivative h'(x) of that point? 2. How to write the proof from the demonstration of this activity?