Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - Review - Exercises - Page 1022: 11


(a) $T_x(6,4)=3.5 ^\circ C/meter$ and $T_y(6,4)=-3.0 ^\circ C/meter$ (b) $D_uT(6,4)=0.35 ^\circ C/meter$ (c) $T_{xy}(6,4)=-0.25$

Work Step by Step

(a) $T_x(6,4)\approx \frac{T(8,4)-T(4,4)}{8-4}=\frac{86-72}{4}=3.5 ^\circ C/meter$ $T_y(6,4)\approx \frac{T(6,6)-T(6,2)}{6-2}=\frac{75-87}{4}=-3.0 ^\circ C/meter$ (b) $D_uT(6,4)\approx \frac{T(8,6)-T(4,2)}{\sqrt {(8-4)^2+(6-2)^2}}=0.35 ^\circ C/meter$ (c) $T_{xy}(6,4)=\frac{T_x(6,6)-T_x(6,2)}{6-2}=\frac{3-4}{4}=-0.25$
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