Calculus (3rd Edition)

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

Chapter 15 - Differentiation in Several Variables - 15.3 Partial Derivatives - Exercises - Page 781: 12

Answer

${f_y}$ is smallest at $C$.

Work Step by Step

${f_y}$ can be approximated by ${f_y} \approx \frac{{\Delta f}}{{\Delta y}}$. This can be calculated by moving up vertically from points $A$, $B$, or $C$ to the next highest level curves. From Figure 8, we see that $\Delta y$ is largest at point $C$ (though $\Delta f$ is twice as much as those of $A$'s and $B$'s but $\Delta y$ is much larger), thus $\frac{{\Delta f}}{{\Delta y}}$ is smallest at $C$. We conclude that ${f_y}$ is smallest at $C$.
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.