Calculus: Early Transcendentals 8th Edition

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: 28

Answer

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

Work Step by Step

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