Proof of Interior Extremum Theorem
Instructions
Use this dynamic activity to explore the proof of the Interior Extremum Theorem using the following function, and you can change the given function as well as the interval (a, b). Move point P to a Min/Max point c of the function on that interval. Construct sequence (xn) so that (xn)c from left (mblue line); (yn)c from right (mred line). Slide n to show terms in (xn) and (yn).
Reflection Questions
Slide n and observe the changes of slopes of mblue line and mred line. What can you conclude from your observation? What properties do values of f(xn)-f(c) have in common? What about values of f(yn)-f(c)? How to write the proof from the demonstration of this activity?