Posted by Soly on .
I don't understand how to do the folliwing problems.
Find and simplify the difference quotient f(x+h) f(x)/h, h cannot equal 0 for the given formula.
1. f(x)=5x^2
options: a. 5, b.5(2x+h), c. 10/h +x+5h, d. 5(2x^2+2xh+h^2)/h
2. f(x)=x^2+3x+9
options: a. 2x+h+9, b.1, c.2x^2+2x+2xh+h^2+h+18/h, d. 2x+h+3

Algebra 
drwls,
Here is how to do #1. #2 is the same.
f(x+h) = 5 (x+h)^2 = 5x^2 + 10 xh + 5h^2
f(x+h)  f(x) = 10xh + 5h^2
[f(x+h)  f(x)]/h = 10 x + 5h = 5x (2+h)
This is answewr # (b)
As h > 0, the ratio approaches 10 x