College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 3 - Section 3.1 - Functions - 3.1 Assess Your Understanding: 84

Answer

$6x+3h-2$

Work Step by Step

We are given: $f(x)=3x^{2}-2x+6$ We find the difference quotient: $\displaystyle \frac{f(x+h)-f(x)}{h}$ $\displaystyle =\frac{[3(x+h)^{2}-2(x+h)+6]-[3x^{2}-2x+6]}{h}$ $\displaystyle =\frac{3(x^{2}+2xh+h^{2})-2x-2h+6-3x^{2}+2x-6}{h}$ $\displaystyle =\frac{3x^{2}+6xh+3h^{2}-2h-3x^{2}}{h}$ $\displaystyle =\frac{6xh+3h^{2}-2h}{h}$ $\displaystyle =\frac{h(6x+3h-2)}{h}$ $=6x+3h-2$
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