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: 44

Answer

$\frac{f(a+h)-f(a)}{h}=6a+3h$

Work Step by Step

We are given: $f(x)=3x^{2}+2$ We evaluate: $f(a)=3a^{2}+2$ $f(a+h)=3(a+h)^{2}+2=3a^{2}+6ah+3h^{2}+2$ $\frac{f(a+h)-f(a)}{h}=\frac{(3a^{2}+6ah+3h^{2}+2)-(3a^{2}+2)}{h}=\frac{6ah+3h^{2}}{h}=\frac{h(6a+3h)}{h}=6a+3h$
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