College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.2: 60

Answer

The difference quotient for the given function is $4x+2h$

Work Step by Step

$f(x)=2x^{2}$ Find the difference quotient $\dfrac{f(x+h)-f(x)}{h}$ Start by finding $f(x+h)$. Substitute $x$ by $x+h$ in $f(x)$ and simplify: $f(x+h)=2(x+h)^{2}=2(x^{2}+2xh+h^{2})=2x^{2}+4xh+2h^{2}$ Substitute the known values into the formula for the difference quotient: $\dfrac{f(x+h)-f(x)}{h}=\dfrac{2x^{2}+4xh+2h^{2}-2x^{2}}{h}=...$ $...=\dfrac{4xh+2h^{2}}{h}=...$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(4x+2h)}{h}=4x+2h$ The difference quotient for the given function is $4x+2h$
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