Write a routine in MATLAB that does the following: given an interval [a, b], a function F, and a number n, your code should produce the following three interpolants to the function F: (i) a polynomial interpolant to F at n equidistant points on [a, b]; (ii) a polynomial interpolant at n Chebyshev points of that interval; (iii) a cubic spline interpolant at n equidistant points. You are allowed to look at our class demo subdir, but you must document this fact (and you may not use the matlab library, such as polyfit). Furthermore, the polynomial interpolation must be done via a table of divided differences.