Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Section 14.3 - Partial Derivatives - 14.3 Exercise: 7

Answer

(a) Positive (b) Negative

Work Step by Step

(a) The second derivative shows concavity. As we move along the x-axis at the point $(-1, 2)$, the graph is shown to be concave up . This shows that $f_{xx} $ is positive. (b) The second derivative shows concavity. As we move along the y-axis at the point $(-1, 2)$, the graph is shown to be concave down. This shows that $f_{yy} $ is negative.
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