1. The problem statement, all variables and given/known data 3. The attempt at a solution Alright so what I did was expanded f(a+h) and f(a+3h) using Taylor Series Expansion. I then said that f'(a) would be some linear combination of f(a), f(a+h) and f(a+3h). I summed up and factored out the terms f(a), f'(a) and f''(a) from the Taylor Series Expansions. Finally for equations 1, I know that I don't want f(a) so c0+c1+c2 = 0. For equation 2, I want to keep f'(a) so that equation is set to equal to 1. For equation 3, I don't want f''(a) so that equation is set to 0. I solved for the coefficients in terms of h and ended up with f'(a) ≈ [f(a+3h) - 33f(a) + 27f(a+h)] / 20h I would like to know if my method and/or answer is correct. My answer in my opinion looks really weird.