5. (extra credit) 10 points repeat problem 3a except using "complex step differentiation." 3. a. (i) Compare the accuracy of the following three formulas for approxi- mating the derivative, f'(x): Mi(n) = f(x + h) f(2) h M2(h) = f(x +h)-f(x h) 2h -f(x + 2h) + 4f (x + h) 3f(x) M3(h) = 2h In particular, test the above approximations when f(x) = 24/3, x = 0 or x = 1, and h = 10-P, p = 3,4,5,..., 20. (ii) Ash is decreased, the error becomes smaller, until a critical value of h is reached, after which point the error starts to increase as h decreases. Find the critical h, herit, experimentally. Note: in order to avoid problems in evaluating 24/3 when x