Problem

You are given the following errorless data set : x = {1, 2, 3, 5 ,7, 8} f(x)={ 3, 6 ,19, 99 , 291, 444}

a. Use nearest neighbour interpolation to find f(x) for the following x values : 2.8, 4.4, and 7.1

b. Implementing MATLAB function or script to perform interpolation based on the closest 2, 3, and 4 points using Lagrangian interpolating polynomials

c. Run your function script on the x values :2.8, 4.4 and 7.1 for the closest 2-, 3-, and 4-point Lagrangian interpolating polynomial