Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 14: Partial Derivatives - Section 14.1 - Functions of Several Variables - Exercises 14.1 - Page 787: 13

Answer

See image. .
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Work Step by Step

Equate $f(x,y)=c$ for each value of c $\left[\begin{array}{llll} c=-3 & x+y-1=-3 & \Rightarrow & y=-x-2 \\ c=-2 & x+y-1=-2 & \Rightarrow & y=-x-1\\ c=-1 & x+y-1=-1 & \Rightarrow & y=-x\\ c=0 & x+y-1=0 & \Rightarrow & y=-x+1\\ c=1 & x+y-1=1 & \Rightarrow & y=-x+2\\ c=2 & x+y-1=2 & \Rightarrow & y=-x+3\\ c=3 & x+y-1=3 & \Rightarrow & y=-x+4 \end{array}\right]$ Lines with slope $-1$, with y-intercepts $-2,-1,...,4$
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