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: 63

Answer

The difference quotient for the given function is $4x+2h+1$

Work Step by Step

$f(x)=2x^{2}+x-1$ 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: $f(x+h)=2(x+h)^{2}+x+h-1=...$ $...=2(x^{2}+2xh+h^{2})+x+h-1=...$ $...=2x^{2}+4xh+2h^{2}+x+h-1$ Substitute the known values into the formula for the difference quotient: $\dfrac{f(x+h)-f(x)}{h}=...$ $...=\dfrac{2x^{2}+4xh+2h^{2}+x+h-1-(2x^{2}+x-1)}{h}=...$ $...=\dfrac{2x^{2}+4xh+2h^{2}+x+h-1-2x^{2}-x+1}{h}=...$ $...=\dfrac{4xh+2h^{2}+h}{h}$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(4x+2h+1)}{h}=4x+2h+1$ The difference quotient for the given function is $4x+2h+1$
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