You are not allowed to use MATLAB built-in functions polyfit, polyval, and spline.

2. (14 points) (Programming by MATLAB) Let f(x) = 1/(1+ 25x2). (b) Using 7 Chebyshev nodes Xi = COS 2i +1 T 2n + 2 i= 0,1,..., n, n= 6 i. find the interpolating polynomial p(x) of degree 6 for f(x) by the Newton approach. ii. find the natural cubic spline function S(x) to interpolate f(x). iii. find the function g(x) = a + bx2 + cx4 to approximate f(x) by the least squares method. Print the coefficients of p(x), S(x) and g(x). Print the four values f(x), f(x) p(x), f(x) S(x), and f(x) g(x) at 13 equally spaced points I; = -1+(1/6)i for i = 0,1,...,12. Plot y = f(x), y = p(x), y = S(x) and y = g(x) on the same plot. 2. (14 points) (Programming by MATLAB) Let f(x) = 1/(1+ 25x2). (b) Using 7 Chebyshev nodes Xi = COS 2i +1 T 2n + 2 i= 0,1,..., n, n= 6 i. find the interpolating polynomial p(x) of degree 6 for f(x) by the Newton approach. ii. find the natural cubic spline function S(x) to interpolate f(x). iii. find the function g(x) = a + bx2 + cx4 to approximate f(x) by the least squares method. Print the coefficients of p(x), S(x) and g(x). Print the four values f(x), f(x) p(x), f(x) S(x), and f(x) g(x) at 13 equally spaced points I; = -1+(1/6)i for i = 0,1,...,12. Plot y = f(x), y = p(x), y = S(x) and y = g(x) on the same plot