Calculus 8th Edition

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

Chapter 14 - Partial Derivatives - 14.6 Directional Derivatives and the Gradient Vector - 14.6 Exercises - Page 997: 29


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

Work Step by Step

Our aim is to determine the maximum rate of change of $f(x,y)$.In order to find this, we have : $D_uf=|\nabla f(x,y)|$ Given: $f(x,y)=x^2+y^2-2x-4y$ $\nabla f(x,y)=\lt 2x-2,2y-4 \gt$ We have found the direction vector as $\lt 1,1 \gt$ or, $\lt 2x-2,2y-4 \gt=n\lt 1,1 \gt$ Hence, $n=2x-2, n=2y-4$ and $2x-2=2y-4$ Therefore, the points at which the direction of fastest change are: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.