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 957: 23


$1, \lt 0,1 \gt$

Work Step by Step

Formula to calculate the maximum rate of change of $f$: $D_uf=|\nabla f(x,y)|$ $\nabla f(x,y)=\lt y \cos xy,x\cos xy \gt $ $\nabla f(1,0)=\lt 0,\cos (0) \gt=\lt 0,1 \gt$ $|\nabla f(0,1)|=\sqrt{0^2+ 1^2}=1$ Hence, the required answers are: $1, \lt 0,1 \gt$
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