College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Section 2.4 - Average Rate of Change of a Function - 2.4 Exercises: 22

Answer

(a) $-\frac{2h}{h+1}$ (b) $-\frac{2}{h+1}$

Work Step by Step

We are given: $g(x)=\frac{2}{x+1}$; $x=0$, $x=h$ (a) We calculate the net change: $g(h)-g(0)=\displaystyle \frac{2}{h+1}-\frac{2}{0+1}=\frac{2}{h+1}-\frac{2(h+1)}{h+1}=-\frac{2h}{h+1}$ (b) We calculate the average rate of change: $\displaystyle \frac{g(h)-g(0)}{h-0}=\frac{-\frac{2h}{h+1}}{h}=\frac{-2h}{h(h+1)}=-\frac{2}{h+1}$
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