How do u approx. the 3rd derivative?
More specifically, how do you derive the following two formulas for approximating the 3rd derivative?
Formula A: f'''(x) ~= [f(x+3h) - 3f(x+2h) + 3f(x+h) - f(x)] / (h^3)
Formula B: f'''(x) ~= [f(x+2h) - 2f(x+h) + 2f(x-h) - f(x-2h)] / (2h^3)
Also what're their respective error terms? And which of the two formula's more accurate? I know you're supposed to use Taylor expansions, etc. but not sure how to exactly. For example, the formula to approx. f'(x) can be found by adding the taylor expansions of f(x+h) and f(x-h) and solving for f'(x).