Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.1 Functions of Two or More Variables - Preliminary Questions - Page 763: 5

Answer

The contour maps of $g\left( {x,y} \right) = 2x$ have larger slope than the contour maps of $f\left( {x,y} \right) = x$.

Work Step by Step

From Exercise 4, we obtain the contour map of $f\left( {x,y} \right) = x$ consists of lines with equation $z=x=c$ for $c = \left( {..., - 2, - 1,0,1,2,...} \right)$, corresponding to the contour interval $1$. Similarly, the contour map of $g\left( {x,y} \right) = 2x$ consists of lines with equation $z=2x=c$ for $c = \left( {..., - 2, - 1,0,1,2,...} \right)$, corresponding to the contour interval $1$. Thus, the contour maps of $g\left( {x,y} \right) = 2x$ have larger slope than the contour maps of $f\left( {x,y} \right) = x$.
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.