Please answer all parts of the question (as they are part of ONE question), and solve in MATLAB.

You are given the following errorless data set: X 12 3 5 7 8 f(x) 36 1999 291 444 a. Use nearest neighbour interpolation to find f(x) for the following x values: 2.8, 4.4, and 7.1 b. Implement a 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 given in a) for the closest 2-, 3-, and 4-point Lagrangian interpolating polynomial You are given the following errorless data set: X 12 3 5 7 8 f(x) 36 1999 291 444 a. Use nearest neighbour interpolation to find f(x) for the following x values: 2.8, 4.4, and 7.1 b. Implement a 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 given in a) for the closest 2-, 3-, and 4-point Lagrangian interpolating polynomial