Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Review Exercises - Page 301: 34

Answer

See the explanation below.

Work Step by Step

(a) f has a relative maximum at c if there is some interval $\left( r,s \right)$ containing c for which $f\left( c \right)\ge f\left( x \right)$ for all $x$ between r and s for which $f\left( x \right)$ is defined. Therefore, at the point $x=0$, the graph gives the relative maximum of $-2$. Hence, the relative maxima occurs at $x=0$, and graph gives the relative maximum of $f\left( 0 \right)=-2$. (b) In case of the interval $\left( r,s \right)$ containing c for which $f\left( c \right)\le f\left( x \right)$ for all $x$ between r and s for which $f\left( x \right)$ is defined, f will have a relative minimum at c. Therefore, at points $-2$ and $3,$ the graph gives the relative minima of $-3,-5,$ respectively. Hence, the relative maxima occurs at $x=-2,3;f\left( -2 \right)=-3,f\left( 3 \right)=-5$ and at points $-2$ and $3,$ the graph gives the relative minima of $-3,-5,$ respectively.
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