In this problem we prove a special case of the MeanValue Theorem where f(a) = f(b)=0
Chapter 4, Problem 44(choose chapter or problem)
In this problem we prove a special case of the MeanValue Theorem where f(a) = f(b)=0. This specialcase is called Rolles Theorem: If f is continuous on[a, b] and differentiable on (a, b), and if f(a) = f(b) =0, then there is a number c, with a < c < b, such thatf(c)=0.By the Extreme Value Theorem, f has a global maximumand a global minimum on [a, b].(a) Prove Rolles Theorem in the case that both theglobal maximum and the global minimum are atendpoints of [a, b]. [Hint: f(x) must be a very simplefunction in this case.](b) Prove Rolles Theorem in the case that either theglobal maximum or the global minimum is not atan endpoint. [Hint: Think about local maxima andminima.]
Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.
Becoming a subscriber
Or look for another answer