Answer
$\frac{f(a+h)-f(a)}{h} = 3a^{2}+3ah+h^{2}$
Work Step by Step
$\frac{f(a+h)-f(a)}{h} = \frac{(a+h)^{3}-a^{3}}{h}
= \frac{a^{3}+3a^{2}h +3ah^{2}+h^{3}-a^{3}}{h}
= \frac{3a^{2}h +3ah^{2}+h^{3}}{h}
= 3a^{2}+3ah+h^{2}$
Calculus: Early Transcendentals 8th Edition
by Stewart, James
Published by
Cengage Learning
ISBN 10:
1285741552
ISBN 13:
978-1-28574-155-0
Chapter 1 - Section 1.1 - Four Ways to Represent a Function - 1.1 Exercises - Page 21: 28
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