3. Consider the interpolation of the function 25r2 +1: 2 (-1, 1). (a) Write a program that computes the coefficients of the Newton form of an interpolating polynomial and that evaluates the resulting polynomial at a vector of points .. (b) Using the code from part (a), produce interpolating polynomials using n evenly spaced data points with n = 3,7, 15. Plot the resulting polynomials. (c) Using the code from part (a), produced interpolating polynomials using n Chebyshev nodes with n = 3,7, 15. Plot the resulting polynomials. (d) Produce a cubic spline interpolant using n evenly spaced data points with n = 3,7, 15. Plot the resulting splines. You may use the built-in Matlab functions spline and ppval