Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.7 Rates of Change in the Natural and Social Sciences - 2.7 Exercises - Page 178: 15

Answer

(a) $S'(1)$ = $8{\pi}$ $ft^{2}/ft$ (b) $S'(2)$ = $16{\pi}$ $ft^{2}/ft$ (c) $S'(3)$ = $24{\pi}$ $ft^{2}/ft$ As the radius increases, the surface area grows at an increasing rate. In fact, the rate of change is linear with respect to the radius.

Work Step by Step

$S(r)$ = $4{\pi}r^{2}$ $S'(r)$ = $8{\pi}r$ (a) $S'(1)$ = $8{\pi}(1)$ = $8{\pi}$ $ft^{2}/ft$ (b) $S'(2)$ = $8{\pi}(2)$ = $16{\pi}$ $ft^{2}/ft$ (c) $S'(3)$ = $8{\pi}(3)$ = $24{\pi}$ $ft^{2}/ft$ As the radius increases, the surface area grows at an increasing rate. In fact, the rate of change is linear with respect to the radius.
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