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: 20


(a) $-3h^{2}-12h$ (b) $-3h-12$

Work Step by Step

We are given: $f(x)=1-3x^2$; $x=2$, $x=2+h$ (a) We calculate the net change: $f(2+h)-f(2)=[1-3(2+h)^{2}]-[1-3(2)^{2}]=[-3h^{2}-12h-11]-[-11]=-3h^{2}-12h$ (b) We calculate the average rate of change: $\displaystyle \frac{f(2+h)-f(2)}{(2+h)-2}=\frac{-3h^{2}-12h}{h}=-3h-12$
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