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