Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 1 - Functions and Their Graphs - Section 1.3 Properties of Functions - 1.3 Assess Your Understanding - Page 75: 61

Answer

(a). $-4$, (b). $-8$, (c). $-10$.

Work Step by Step

(a). From $x_1=0$ to $x_2=2$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(2)^2+4)-(-2(0)^2+4)}{2-0}=\frac{-8}{2}=-4$, (b). From $x_1=1$ to $x_2=3$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(3)^2+4)-(-2(1)^2+4)}{3-1}=\frac{-16}{2}=-8$, (c). From $x_1=1$ to $x_2=4$, we have the average rate of change as $\frac{f(x_2)-f(x_1)}{x_2-x_1}=\frac{(-2(4)^2+4)-(-2(1)^2+4)}{4-1}=\frac{-30}{3}=-10$.
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