Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Section 14.6 - Directional Derivatives and the Gradient Vector - 14.6 Exercise - Page 956: 3

Answer

$\approx 0.778$

Work Step by Step

$D_uf=f_x(x,y)a+f_y(x,y)b$ $D_uf=\dfrac{-39-(-26))}{-25-(-15)} \times \dfrac{1}{\sqrt2}+\dfrac{-34-(-30))}{40-20} \times \dfrac{1}{\sqrt2}$ This implies $D_uf=\dfrac{13}{10} \times \dfrac{1}{\sqrt2}+\dfrac{-1}{5} \times \dfrac{1}{\sqrt2}$ $D_uf \approx 0.778$
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