Please program in Java

a. Write a program that takes any n + 1 distinct points and returns the coefficients a_k , k = 0,1,..., n for the Newton form of the interpolating polynomial for a function f(x).

b. Write a program that takes the Newton coefficients of the polynomial and a point x and evaluates P_n(x).

c. Apply the the two programs to compute the interpolant to f(x) = 1/(1 + 25x²) and do the following:

(i) Using the 21 uniformly spaced nodes x_k= -1 + k(.1) ,k= 0,1, ... ,20 have your program compute the error at x=.985.

( ii) Using 21 Chebyshev nodes given by x_k= cos((2k+ 1) / 2(20 + 1)) ,k= 0,1, ... ,20. Have your program compute the error at x=.985. The output of your program should be the error in each case.