# Find and simplify the different quotient f(x+h)-f(x) / h f(x)=-x^2+5x+5 f(x+h)-f(x) / h =????

User Generated

parjzna12512

Mathematics

### Question Description

Find and simplify the different quotient f(x+h)-f(x) / h

f(x)=-x^2+5x+5

f(x+h)-f(x) / h =????

Student has agreed that all tutoring, explanations, and answers provided by the tutor will be used to help in the learning process and in accordance with Studypool's honor code & terms of service.

$f(x)=-x^2+5x+5\\ \\ f(x+h)=-(x+h)^2+5(x+h)+5\\ \\ f(x+h)=-(x^2+2xh+h^2)+5x+5h+5\\ \\ f(x+h)=-x^2-2xh-h^2+5x+5h+5\\ \\ f(x+h)-f(x)=-x^2-2xh-h^2+5x+5h+5-(-x^2+5x+5)\\ \\ f(x+h)-f(x)=-x^2-2xh-h^2+5x+5h+5+x^2-5x-5\\ \\ f(x+h)-f(x)=-2xh-h^2+5h\\ \\$

Difference quotient is

$\frac{f(x+h)-f(x)}{h}=\frac{-2xh-h^2+5h}{h}\\ \\ \frac{f(x+h)-f(x)}{h}=\frac{h(-2x-h+5)}{h}\\ \\ \frac{f(x+h)-f(x)}{h}=-2x-h+5\\$

-------------------------------------------------------------

fulnzanve3 (279)
Carnegie Mellon University
Review
Review

Anonymous
Just what I needed…Fantastic!

Studypool
4.7
Trustpilot
4.5
Sitejabber
4.4