SOLUTION: Find the difference quotient and simplify for the following function: f(x)=-10x^2 + 10x +8. Thanks for your help.

Algebra ->  Equations -> SOLUTION: Find the difference quotient and simplify for the following function: f(x)=-10x^2 + 10x +8. Thanks for your help.      Log On


   

Question 994056: Find the difference quotient and simplify for the following function: f(x)=-10x^2 + 10x +8. Thanks for your help.
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
h, some small quantity which can be made as small as you wish be never being 0.

f%28x%2Bh%29=-10%28x%2Bh%29%5E2%2B10%28x%2Bh%29%2B8
-10%28x%5E2%2B2hx%2Bh%5E2%29%2B10x%2B10h%2B8
-10x%5E2-20hx-10h%5E2%2B10x%2B10h%2B8



Difference Quotient is
%28f%28x%2Bh%29-f%28x%29%29%2Fh

%28%28-10x%5E2-20hx-10h%5E2%2B10x%2B10h%2B8%29-%28-10x%5E2+%2B+10x+%2B8%29%29%2Fh
%28-10x%5E2-20hx-10h%5E2%2B10x%2B10h%2B8%2B10x%5E2-10x-8%29%2Fh, look at the terms in the numerator carefully....
%28-20hx-10h%5E2%2B10h%29%2Fh
highlight%28-20x-10h%2B10%29
You might then ask, "what happens as h approaches 0?"