Answer
$\frac{dy}{dt}=-\frac{1}{2}$
Work Step by Step
$8y^{3} + x^{2}= 1$
$24y^{2}\frac{dy}{dt}+2x\frac{dx}{dt}=0$
Now substitute x = 3, y = -1, and dx/dt =2 to get
$24(-1)^{2}\frac{dy}{dt}+2(3)(2)=0$
$\frac{dy}{dt}=-\frac{1}{2}$
Calculus with Applications (10th Edition)
by Lial, Margaret L.; Greenwell, Raymond N.; Ritchey, Nathan P.
Published by
Pearson
ISBN 10:
0321749006
ISBN 13:
978-0-32174-900-0
Chapter 6 - Applications of the Derivative - 6.5 Related Rates - 6.5 Exercises - Page 341: 2
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