For a given set of discrete data points (x_i, f_i) (i = 0, 1, 2, . . . , n), show that the coefficients a_k (k = 0, 1, . . . , n) fitted to the polynomial

are given by the solution of the equations written in matrix form as

The following data is taken from the tables of the Airy function f(x) = Ai(–x):

Estimate from the polynomial approximation the values of f(2.0) and f (3.5).