Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 1 - Graphs - 2.1 Functions - 2.1 Assess Your Understanding - Page 58: 82



Work Step by Step

RECALL: $\\\\$The difference quotient of a function $f$ is given by the formula $\dfrac{f(x+h)-f(x)}{h}$ where $h \ne0$. Use the difference quotient formula above to obtain: $\dfrac{f(x+h)-f(x)}{h}\\ =\dfrac{[3(x+h)^2+2]-(3x^2+2)}{h}\\ =\dfrac{[3(x^2+2xh+h^2)+2]-(3x^2+2)}{h}\\ =\dfrac{3x^2+6xh+3h^2+2-3x^2-2}{h}\\ =\dfrac{6xh+3h^2}{h}\\ =\dfrac{h(6x+3h)}{h}\\ =6x+3h$
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