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: 24


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

Work Step by Step

We are given: $f(t)=\sqrt{t}$; $t=a$, $t=a+h$ (a) We calculate the net change: $f(a+h)-f(a)=\sqrt{a+h}-\sqrt{a}$ (b) We calculate the average rate of change: $\displaystyle \frac{f(a+h)-f(a)}{(a+h)-a}=\frac{\sqrt{a+h}-\sqrt{a}}{h}*\frac{\sqrt{a+h}+\sqrt{a}}{\sqrt{a+h}+\sqrt{a}}=\frac{(a+h)-a}{h(\sqrt{a+h}+\sqrt{a})}=\frac{h}{h(\sqrt{a+h}+\sqrt{a})}=\frac{1}{\sqrt{a+h}+\sqrt{a}}$
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