Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 14 - Partial Derivatives - 14.1 Exercises - Page 913: 23

Answer

Please see image below.

Work Step by Step

1. No x in the equation, no intercept with the x-axis. 2. Set $x=0$. The trace is a line ($z=1+y$). Find intercepts with the y and z-axes. $f(0,0)=1$, so the z intercept is at $(0,0,1)$ When $z=f(x,y)=0$, $0=1+y$ $y=-1$. so the y-intercept is at $(0,-1,0).$ 3. Sketch a line through the intercepts (in the yz plane), 4. Sketch lines through the intercepts, parallel to x 5. The result is a plane.
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