Hello, I am struggling with writing the Matlab code for the problem statement posted below, any help that can be provided would be greatly appreciated. Thank you

Problem Statement:

Write an algorithm for calculating coefficients of the Newtons interpolating polynomial function for a given discrete data set. This specific problem will demonstrate the case that a more number of given data may result in poor curve fitting when the data are in fact from a smooth curve. Submit your m-file and the figure.

Write an algorithm that interpolates given data points using the Newtons interpolating polynomial. Your algorithm must be a function that takes data points as inputs and outputs the coefficients via completing the divided-difference table.

Using the above algorithm, fit the following two data sets and plot the results in a single figure plotting Data 1 in blue circle, the corresponding interpolating polynomial for Data 1 in black line, Data 2 in red triangle, and the corresponding interpolating polynomial for Data 2 in black dashed line.

Data set 1: x = [1, 0.5, 0, 0.5, 1] f(x) = [0.0385, 0.1379, 1.0000, 0.1379, 0.0385]

Data set 2: x = [1, 0.75. 0.5, 0.25, 0, 0.25, 0.5, 0.75, 1] f(x) = [0.0385, 0.0644, 0.1380, 0.3902, 1.0000, 0.3902, 0.1380, 0.0644, 0.0385]