Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 14 - Partial Derivatives - Review - Concept Check - Page 1021: 18


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

Work Step by Step

a) It consists of all the boundary or critical points and when one or more than one points does not exist in a boundary but the set should remains open or should not be closed. A bounded set is defined as the set that bounds itself in the disk and is finite. b) Extreme value theorem states that suppose $f(x,y)$ is a continuous and bounded set in a closed set of real numbers in domain $D$ whose absolute maximum values such as $f(x_1,y_1)$ and absolute minimum values such as $f(x_2,y_2)$ in the real numbers of domain $D$. c) i) Critical point of $f(x,y)$ in the domain $D$. ii) Extreme values of $f(x,y)$ in the domain $D$. iii) Absolute maximum and absolute minimum values of $f(x,y)$ in the domain $D$.
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