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: 3

Answer

-15

Work Step by Step

$y = -3x^{3} + 2x^{2} - 4x + 1$ between x = -2 and x = 1 To find the rate of change, you have to use the rate of change formula: $\frac{f(b)−f(a)}{b−a}$ In this problem, the starting point is -2 and the end point is 1. Therefore, a = -2 and b = 1. Since you know the a and b values, you can plug them into the formula: $\frac{(-3\times (1)^{3}+2\times 1^{2}-4(1)+1) - (-3\times (-2)^{3}+2\times -2^{2}-4(-2)+1) }{1-(-2)}$ = $\frac{(-4)-(41)}{3}$ = $\frac{-45}{3}$ = -15 Therefore, the average rate of change is -15.
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