Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Review - Concept Check - Page 981: 18


a) See the explanation below. b) See the explanation below. c) See the explanation below.

Work Step by Step

a) A closed set in $R^2$ is one that contains all of its boundary points. A bounded set is one that is contained within some disk (finite in extent). b) The extreme value theorem states the following. Suppose $f(x,y)$ is continuous on a closed and bounded set D in $R^2$. We can then state that $f$ attains absolute maximum values $f(x_1,y_1)$ and absolute minimum values $f(x_2,y_2)$ at some points in D. c) See section 9 of 14.7. i) Find the critical point of $f(x,y)$ in the domain $D$. ii) Find the extreme values of $f(x,y)$ in the domain $D$. iii) Compare i and ii for the largest (Absolute maximum) and smallest (absolute minimum) values.
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