Machine precision = 1E-16. Will rate immediately for thorough answer.

Suppose you have an O(hP) accurate formula f(m)() ~ cf(x + axh) k to estimate an m-th derivative f(m) (2), where f is computed to machine precision. Give a reasonable estimate for the h you should try when using the formula, assuming you want the best accuracy. Hint: why do the cx's have to be a constant divided by hm?. Also give the corresponding estimate for the best error you can expect to get. Suppose you have an O(hP) accurate formula f(m)() ~ cf(x + axh) k to estimate an m-th derivative f(m) (2), where f is computed to machine precision. Give a reasonable estimate for the h you should try when using the formula, assuming you want the best accuracy. Hint: why do the cx's have to be a constant divided by hm?. Also give the corresponding estimate for the best error you can expect to get