Calculus (3rd Edition)

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

Chapter 4 - Applications of the Derivative - Chapter Review Exercises - Page 221: 9


$$L(r) =36\pi(r-2)$$

Work Step by Step

Given $$A(r)=\frac{4}{3} \pi r^{3}, \quad a=3$$ Since \begin{align*} A^{\prime}(r)&=4\pi r^2 \\ A^{\prime}(3)&= 36\pi \end{align*} Then the linear approximation is given by \begin{align*} L(r)&=A^{\prime}(a)(r-a)+A(a)\\ &= 36\pi(r-3)+ 36\pi\\ &=36\pi(r-2) \end{align*}
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.