Because the derivative of f may not be continuous.

(But the same ideas that we use to sidestep the need for the Intermediate Value Theorem in this proof are used in the Intermediate Value Theorem for Derivatives to show that even when the derivative of a function isn't continuous, the results of the Intermediate Theorem often still hold.)

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