Find a more accurate formula for f'(t) using method of undetermined coefficient. Let's say the formula is of the form
f'(t) = A f ( t + 2h ) + B f ( t + h ) - B f ( t - h ) - A f ( t - 2h )
Find the values of A and B such that error is minimized. What power of h is the error proportional to? Use this formula to find
d/dx sin(x) at x = pi/3. Tabulate errors for different values of h.