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: 68

Answer

The difference quotient for the given function is $-6x-3h+2$

Work Step by Step

$f(x)=-3x^{2}+2x-1$ 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: $f(x+h)=-3(x+h)^{2}+2(x+h)-1=...$ $...=-3(x^{2}+2xh+h^{2})+2x+2h-1=...$ $...=-3x^{2}-6xh-3h^{2}+2x+2h-1$ Substitute the known values into the formula for the difference quotient: $\dfrac{f(x+h)-f(x)}{h}=...$ $...=\dfrac{-3x^{2}-6xh-3h^{2}+2x+2h-1-(-3x^{2}+2x-1)}{h}=...$ $...=\dfrac{-3x^{2}-6xh-3h^{2}+2x+2h-1+3x^{2}-2x+1}{h}=...$ $...=\dfrac{-6xh-3h^{2}+2h}{h}=...$ Take out common factor $h$ from the numerator and simplify: $...=\dfrac{h(-6x-3h+2)}{h}=-6x-3h+2$ The difference quotient for the given function is $-6x-3h+2$
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.