CALCULUS Understanding Its Concepts and Methods

Local maximum

A function
*f*
has a local maximum at a point
*a*
if
*f*(*a*) ≥ *f*(*x*)
for every point
*x*
that is sufficiently near
*a*.

A local maximum is also called a relative maximum.

A maximum is sometimes called an absolute maximum to emphasize that it is not just a relative maximum.

In order to say that
*f*
has a local maximum or minimum at
*a*,
we require that
*f*
be defined on all points that are sufficiently close to
*a*.

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.