Thread: 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.

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))?

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(h²)

Is this some kind of numerical quadrature scheme?

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.