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: 19


(a) $5h^{2}+30h$ (b) $5h+30$

Work Step by Step

We are given: $f(t)=5t^2$; $t=3$, $t=3+h$ (a) We calculate the net change: $f(3+h)-f(3)=[5(3+h)^{2}]-[5(3)^{2}]=45+30h+5h^{2}-45=5h^{2}+30h$ (b) We calculate the average rate of change: $\displaystyle \frac{f(3+h)-f(3)}{(3+h)-3}=\frac{5h^{2}+30h}{h}=\frac{h(5h+30)}{h}=5h+30$
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