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 - Page 224: 23


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

Work Step by Step

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