Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 3 - The Derivative - 3.3 Rates of Change - 3.3 Exercises - Page 158: 4



Work Step by Step

y = $2x^{3} - 4x^{2} + 6x$ between x = -1 and x = 4 To find the rate of change, you have to use the rate of change formula: f(b)−f(a)b−a In this problem, the starting point is -1 and the end point is 4. Therefore, a = -1 and b = 4. Since you know the a and b values, you can plug them into the formula: $\frac{(2(4)^3-4(4)^2+6(4))-(2(-1)^3-4(-1)^2+6(-1))}{4-(-1)}$ = $\frac{88-(-12)}{5}$ = $\frac{100}{5}$ = 20 Therefore, the average rate of change is equal to 20.
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