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: 65

Answer

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

Work Step by Step

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

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.