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: 29


All the points on the line $y=x+1 $

Work Step by Step

Formula to calculate the maximum rate of change of $f$: $D_uf=|\nabla f(x,y)|$ $\nabla f(x,y)=\lt 2x-2,2y-4 \gt$ Direction vector: $\lt 1,1 \gt$ Thus, $\lt 2x-2,2y-4 \gt=n\lt 1,1 \gt$ This implies $n=2x-2, n=2y-4$ and $2x-2=2y-4$ Hence, the required answer is: All the points on the line $y=x+1 $
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.