Calculus: Early Transcendentals 8th Edition

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

Chapter 14 - Section 14.4 - Tangent Planes and Linear Approximation - 14.4 Exercise: 4

Answer

$z = 1/4x+y-2$

Work Step by Step

Question: $z = x / y^{2}$, $(-4,2,-1)$ The equation of the tangent plane to the surface is: $z - z_{0} = f_{x}(x_{0},y_{0})(x - x_{0}) + f_{y}(x_{0},y_{0})(y - y_{0})$ $f_{x} = (y^{2}*1 - x * 0) / ((y^{2})^{2}$ = $1/y_{2}$ (use the quotient rule) so $f_{x}(-4,2) = 1/4$ $f_{y} = (y^{2}*0 - x * 2y) / ((y^{2})^{2}$ = $(-2xy)/y_{4}$ (use the quotient rule) so $f_{y}(-4,2) = 1$ So the equation is: $z + 1 = 1/4*(x+4) + 1(y-2)$ And the final answer is: $z = 1/4x+y-2$
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.