Please use MATLab to implement the following Cubic Splines Method WITHOUT use of built-in MATLab spline function. Input is read in from a text file.

Cubic Splines: Given a set of points find the coefficients of all the 3rd degree polynomials that go through all the given points using the cubic splines method. Input: Sample input representing the points (1, 5), (2, 6), (3, 6.5), (4, 5.5), (5, 5.5), (6, 7) 6 1 5 2 6 3 6.5 4 5.5 5 5.5 6 7 where the first number corresponds to the number of points. Output: (a) Coefficients of n1 polynomials. The coefficients of each polynomial in a row separated by spaces (see lecture notes for lecture 14): 5 1.014354 0 -0.014354 6 0.971291667 -0.043062 -0.42822967 6.5 -0.39952167 -1.327751 0.727272667 5.5 -0.87320567 0.854067 0.019138667 5.5 0.89234467 0.911483 -0.30382767 (b) A plot like the one shown:

3 2 0 3 2 0