Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 3 - Section 3.9 - Related Rates - 3.9 Exercises - Page 249: 12

Answer

The x-coordinate is increasing at a rate of $6~cm/s$

Work Step by Step

We can differentiate both sides of the equation with respect to $t$: $xy = 8$ $y~\frac{dx}{dt}+x~\frac{dy}{dt} = 0$ $y~\frac{dx}{dt} = -x~\frac{dy}{dt}$ $\frac{dx}{dt} = -\frac{x}{y}~\frac{dy}{dt}$ $\frac{dx}{dt} = (-\frac{4}{2})~(-3~cm/s)$ $\frac{dx}{dt} = 6~cm/s$ The x-coordinate is increasing at a rate of $6~cm/s$.
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