|
Question 660028: Find and simplify the difference quotient of f,
f(x) = x^2+ 8x + 5
F(x+h)-F(x)
all over
h
Answer by math-vortex(648)   (Show Source):
You can put this solution on YOUR website!
Hi, there--
The Problem:
Find and simplify the difference quotient of f,
f(x) = x^2+ 8x + 5
F(x+h)-F(x)
all over h
A Solution:
Difference quotients can seem VERY tedious. In addition, it is easy to make a computation
error when you simplify them. When I first learned about difference quotients, my teacher
didn't tell me why they were such a big deal. I now know that they are helpful later in
understanding and calculating derivatives in calculus. (I personally don't mind doing tedious
math zoo much if I know it will be helpful later.) Anyway...
f(x) = x^2 + 8x + 5
f(x+h) = (x+h)^2 + 8(x+h) + 5
[f(x+h) - f(x)]/h = {[(x+h)^2 + 8(x+h) + 5] - [x^2 + 8x + 5]}/h
= {[x^2 + 2xh + h^2 +8x + 8h + 5] - [x^2 + 8x + 5]}/h
= {x^2 + 2xh + h^2 +8x + 8h + 5 - x^2 - 8x - 5]}/h
= {2xh + h^2 + 8h]}/h
= 2x + h + 8
If this is unclear, or you still have questions, feel free to email.
Mrs.Figgy
math.in.the.vortex@gmail.com
|
|
|
| |
