$3\mathrm{.}2\mathrm{.}2\mathrm{.}2$ Data interpolation

Download the file lagrange$\_$data.txt from the VLE $($the data represents $5$ data points$)$ and read in the data points using loadtxt.

Plot, in the same figure, all Lagrange polynomials, $L_k(x),$ corresponding to the data provided. Discuss the properties of these functions.

Make a second plot showing, in the same figure, the discrete data provided and the corresponding interpolating polynomial, $P(x).$ Comment on your results.