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: 59

Answer

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

Work Step by Step

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