Calculus: Early Transcendentals 8th Edition

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

Chapter 16 - Section 16.1 - Vector Fields - 16.1 Exercise - Page 1074: 31


Plot $II$

Work Step by Step

The level sets of $f$ are of the form of $x+y=c$ for $c\geq 0$, so they are parallel lines. The vector filed must be perpendicular to all of these, which leaves $II$ as the only possible plot. Hence, only plot $II$ satisfies these conditions.
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