please help: Find the coefficients a₀ a₁ a₂ a₃
such that
a₀f(x-2h)+a₁f(x-h)+a₂f(x+h)+a₃f(x+2h) = f'(x) +O(h⁴)
for any smooth function f. Check your answer with
f(x) = (e^x)(cos(x) at x = 0. Use several values of h and show numerically that the degree of accuracy of the formula that you have obtained is correct.
thanks