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 - Page 925: 73


$\approx 12.2$, $\approx 16.8$, and $\approx 23.25$ See explanation below.

Work Step by Step

The rate of change in the x-direction is given as: $f_x(3,2)=\dfrac{22.4-10.2}{3.5-2.5} \approx 12.2$ When $(x,y) =(3,2.2)$, then we have: $f_x(3,2.2)=\dfrac{26.1-9.3}{3.5-2.5} \approx 16.8$ When $(x,y) =(3,2)$, then we have: $f_{xy}(3,2)=\dfrac{(26.1-9.3)-(20.0-12.5)}{2.2-1.8} \approx 23.25$ Hence, our required answers are: $\approx 12.2 \\ \approx 16.8 \\\approx 23.25$
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