Of course there's no reason why the function should just be continuous on [a,b], or just be differentiable on (a,b). In fact, usually, f will be differentiable (and hence continuous) on a much larger set E, and a and b are just going to be two points that we pick in E (with the additional property that the whole interval [a,b] lies inside E.)

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