College Algebra 7th Edition

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

Chapter 2, Functions - Chapter 2 Review - Exercises - Page 268: 56


Net change: $2ah+2h+h^{2}$ Average rate of change: $2a+2+h$

Work Step by Step

We find the net change from $x=a$ to $x=a+h$: $g(a+h)-g(a)=(a+h+1)^{2}-(a+1)^{2}=(a^2+ah+a+ha+h^2+h+a+h+1)-(a^2+2a+1)=2ah+2h+h^{2}$ Next we find the average rate of change for this interval: $\frac{g(a+h)-g(a)}{a+h-a}=\frac{2ah+2h+h^{2}}{h}=\frac{h(2a+2+h)}{h}=2a+2+h$
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