The key ingredient in this proof is the Mean Value Theorem. This ought not to be surprising; the Mean Value Theorem is the tool we always use to pass from information about the derivative of a function at points (``local information'') to deduce facts about the behavior of the function as a whole (``global information''). For example, it was the Mean Value Theorem which we already used to prove that when the derivative is positive, then the function is increasing.

Analysis WebNotes by John Lindsay Orr.
Comments to the author: jorr@math.unl.edu

All contents copyright (C) 1996 John L. Orr
University of Nebraska--Lincoln
All rights reserved

Last modified: May 1996