Answer
$y=9x^{1/3}+4$
Work Step by Step
The anti-derivative for $\dfrac{dy}{dx}=3x^{-2/3}$ is $y=9x^{1/3}+C$
Apply the initial conditions $y(-1)=-5$.
This implies $-9+C=-5$
or, $C=4$
Hence, $y=9x^{1/3}+4$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 4: Applications of Derivatives - Section 4.7 - Antiderivatives - Exercises 4.7 - Page 240: 75
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