CALCULUS Understanding Its Concepts and Methods

Extreme values

The maximum value and the minimum value of a function
*
f*
on a set
*S*
are called its extreme values.

The maximum value of a function
*
f*
on a set
*S*
is a number
*M*
such that

**1.** *f*(*x*)* *
≤
*M* for every
*x* in *
S*, and

**2.** *f*(*x*) =
*M *for some
*x* in *
S*.

A function
*
f*
achieves its maximum value
*M*
at
*x*
if
*f*(*x*) = *
M*.

The minimum value of a function
*
f*
on a set
*S*
is a number
*m*
such that

**1.** *f*(*x*)
≥ *m* for every
*x* in *
S*, and

**2.** *f*(*x*) =
*m *for some
*x* in *
S*.

The function
*
f*
achieves its minimum value
*m*
at
*x*
if
*f*(*x*) = *
m*.

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

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.