1. Given a function f and a value x the purpose of this exercise is to evaluate the accuracy of the quantity -f(x - 2h) + 16f(x-h)-30f()16f (x +h) - f(z + 2h) 12h2 as an approximation of a derivative of f at x a) (6 pts) which derivative off at z does Q(h) approximates as h 0? b) (8 pts) Write a Perl code to determine the optimal value of h numerically on a computer with machine epsilon . c (6 pts) Justify the results by considering roundoff and truncation errors