College Algebra 7th Edition

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

Chapter 2, Functions - Section 2.1 - Functions - 2.1 Exercises: 50

Answer

$\frac{f(a+h)-f(a)}{h}=3a^{2}+3ah+h^{2}$

Work Step by Step

We are given: $f(x)=x^3$ We evaluate: $f(a)=a^{3}$ $f(a+h)=(a+h)^{3}=a^{3}+3a^{2}h+3ah^{2}+h^{3}$ $\frac{f(a+h)-f(a)}{h}=\frac{(a^{3}+3a^{2}h+3ah^{2}+h^{3})-(a^{3})}{h}=\frac{3a^{2}h+3ah^{2}+h^{3}}{h}= \frac{h(3a^{2}+3ah+h^{2})}{h}=3a^{2}+3ah+h^{2}$
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