Let f(1) = 1 + 6.12 (a) Write a program to perform Lagrange polynomial interpolation at the uniform points and the Chebyshev points on the interval (-1,1] for f. (b) Write a program to perform natural cubic spline interpolation at the uniform points for Investigate the convergence by running the program for different values of n. In the write up include plots of f, Ln, Sn for n = 8, 16, 32. Answer the following questions, Does In converge uniformly to f on [-1, 1]? Does Sn converge uniformly to f on [-1, 1]? Let f(1) = 1 + 6.12 (a) Write a program to perform Lagrange polynomial interpolation at the uniform points and the Chebyshev points on the interval (-1,1] for f. (b) Write a program to perform natural cubic spline interpolation at the uniform points for Investigate the convergence by running the program for different values of n. In the write up include plots of f, Ln, Sn for n = 8, 16, 32. Answer the following questions, Does In converge uniformly to f on [-1, 1]? Does Sn converge uniformly to f on [-1, 1]