Math Help......how to evaluate and simplify this problem?

Question

I need to evaluate:

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

and simplify if:

f(x) = x^2 - 2x

I don't need the answer, but just how to attempt this problem. I know that I need to replace x with x^2 - 2x, but Im not sure what to do with the variable h. Thank You.

Answer 1

f(x) = x^2 - 2x
f(x + h) = (x + h)^2 - 2(x + h) [just plug x+h into f(x) for every x]

f(x + h) - f(x)
= [(x + h)^2 - 2(x + h)] - [x^2 - 2x]
Expand:
= [x^2 + 2xh + h^2 - 2x - 2h] - [x^2 - 2x]
Simplify:
= 2xh + h^2 - 2h

[f(x + h) - f(x)] / h
= (2xh + h^2 - 2h) / h
= (2xh)/h + (h^2)/h - (2h)/h
= 2x + h - 2

Answer 2

this is precalculus
first you need to plug in the function into the f(x + h) - f(x) / h
so
(x+h)^2 -2(x=h)- x^2 - 2x/h
= 2x+2 +h

Answer 3

And if you take the limit of the answer as h goes to 0, you end up with the derivative of f(x).

Answer 4

G(x)=f(y) -f(x)/h
.
where,,,
y=x+h and f(x)=x^2 -2 x
.