Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 14 - Section 14.6 - Directional Derivatives and the Gradient Vector - 14.6 Exercise - Page 1006: 20

Answer

$-2.83$

Work Step by Step

Formula to calculate the directional derivative: $D_uf=\nabla f(x,y) \cdot u$ or, $D_uf=\nabla f(x,y) \cdot \dfrac{v}{|v|}$ From the given figure, we have $\theta=180^\circ+45^\circ=225^\circ$ or, $\dfrac{5\pi}{4}$ At $(2,2)$ $D_uf (2,2)=(4)(1) \cdot \dfrac{5\pi}{4}$ Hence, $D_uf (2,2)=-2.83$
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