Calculus (3rd Edition)

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

Chapter 3 - Differentiation - 3.4 Rates of Change - Exercises - Page 129: 2


75 square units per unit

Work Step by Step

First, we note that the equation for volume of a cube to be: $$V=s^3$$ By taking the derivative of both sides we get: $$V′=3s^2$$ When s = 5, the rate of change, or the derivative at that specific point is: $$V′(5)=3(5^2)=3(25) = 75\ square\ units\ per\ unit$$
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