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: 67

Answer

The difference quotient for the given function is $-4x-2h+5$

Work Step by Step

$f(x)=-2x^{2}+5x+7$ 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: $f(x+h)=-2(x+h)^{2}+5(x+h)+7=...$ $...=-2(x^{2}+2xh+h^{2})+5x+5h+7=...$ $...=-2x^{2}-4xh-2h^{2}+5x+5h+7$ Substitute the known values into the formula for the difference quotient: $\dfrac{f(x+h)-f(x)}{h}=...$ $...=\dfrac{-2x^{2}-4xh-2h^{2}+5x+5h+7-(-2x^{2}+5x+7)}{h}=...$ $...=\dfrac{-2x^{2}-4xh-2h^{2}+5x+5h+7+2x^{2}-5x-7}{h}=...$ $...=\dfrac{-4xh-2h^{2}+5h}{h}=...$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(-4x-2h+5)}{h}=-4x-2h+5$ The difference quotient for the given function is $-4x-2h+5$
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