Finding Second-Order First Derivative

I can't figure out how to find the second-order first derivative. Do I start with the central difference formula, or the forward/backward difference formulas?

This is what I'm trying to derive: f'(x) = [-f(x+2h) + 4f(x+h) - 3f(x)] / 2h

I know the finite difference formula is: f'(x) = [f(x+h) - f(x)] / h

I thought that I might be able to use some formulas found on this page: Numerical Methods/Numerical Differentiation - Wikibooks

Anyway, I'm stuck, and any help would be appreciated.

Re: Finding Second-Order First Derivative

Hey crossingdouble.

Are you trying to find an expression for f''(x) instead of f'(x) (since you have given the difference equation for f'(x))?

Re: Finding Second-Order First Derivative

No, it is for f'(x). The problem says: *Prove the second-order formula for the first derivative.*

f'(x) = [-f(x+2h) + 4f(x+h) - 3f(x)] / 2h + O(h^{2})

Re: Finding Second-Order First Derivative

Is this some kind of numerical quadrature scheme?

Re: Finding Second-Order First Derivative

Sorry for the late response. No, I don't think this is numerical quadrature. The section in my textbook said numerical differentiation. Although, I think the next section deals with adaptive quadrature. Anyway, I think this problem requires the mean value theorem and Taylor series as well. I think it's going to be more drawn out than I expected, so I'm just going to go ask my professor.