Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.1 - Functions of Several Variables - Exercises 14.1 - Page 787: 15

Answer

See image. .
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Work Step by Step

Equate $f(x,y)=c$ for each value of c $ xy=c\quad$or For $c=0, $ we have the origin. For the other values of c, $y=\displaystyle \frac{c}{x}$ is a family of hyperbolas related to $y=\displaystyle \frac{1}{x}$, by performing reflections about the x-axis and vertical stretching.
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