Sorry... need some more help...?

Question

Ok, so I asked this question last night, and thought I understood it, but there's 2 parts I can't seem to get...

[f(x+h) - f(x)] / h
Where A. f(x) = 1 / (x + 1) ; B. f(x) = x^2

Sorry but I just don't understand this stuff... help??

Answer 1

Well, this is calculus related staff.
(A) f(x) = 1 / (x + 1)
[f(x+h) - f(x)] / h = {1 / (x+h + 1) - 1 / (x + 1)}/h
= (x+1 -x-h-1)/{h(x+h + 1)(x + 1)}
= -1/{(x+h + 1)(x + 1)}
(B) f(x) = x^2
[f(x+h) - f(x)] / h = {(x+h)^2 -x^2}/h
= (2hx + h^2)/h
= 2x + h
For any size h, these calculation is not that important. It is important only when h approaches zero. df/dx is defined as
[f(x+h) - f(x)] / h when h approaches zero. In this case:
(A) df/dx = -1/(x+1)^2
(B) df/dx = 2x