Which do you expect to give the better approximation of any old function f[x] on an interval [b - 2, b + 2]: expan2[x, b] = f[b] + f'[b] (x - b) + (1/2) Derivative[1][f'][b] (x - b)^2 or fmidpt[x, b] = f[b] + f'[(x + b)/2] (x - b) ?
Which do you expect to give the better approximation of any old function f[x] on an interval b- 2, b+2] expan2 [x, b] = f[b] + f' [b] (x-b)-. (f')' [b] (x-b) of
