Question

find and simplify each of the following for f(x)=5x^2−6x+8.

A) f(x+h)
B) f(x+h)-f(x)
C) )(f(x+h)-f(x))/h

Answer 1

f(x+h) = 5(x+h)^2 - 6(x+h) + 8 = 5x^2 + 10xh + 5h^2 - 6h - 6x + 8
and I think you can manage the rest, right? It's just Algebra I.
Post your work if you get stuck.

Answer 2

Looks like you are learning "derivatives from First Principles"

f(x)=5x^2−6x+8

f(x+h) = 5(x+h)^2 - 6(x+h) + 8
= 5x^2 + 10hx + 5h^2 - 6x - 6h + 8

f(x+h)-f(x) = 5x^2 + 10hx + 5h^2 - 6x - 6h + 8 - (5x^2 - 6x + 8)
= 5x^2 + 10hx + 5h^2 - 6x - 6h + 8 - 5x^2 + 6x - 8
= 10hx + 5h^2 - 6h

(f(x+h)-f(x))/h
= (10hx + 5h^2 - 6h)/h
= 10x + 5h - 6

I bet your next step in this section will be to take
lim 10x + 5h - 6 , as h ----> 0

Answer 3

Didn't see oobleck aready did this