Question $[12$ Points$]$

Given the function $f(x)=logx,$ and the following data points:

$\backslash$table$[[x,4\mathrm{.}0,4\mathrm{.}5,5\mathrm{.}5,6\mathrm{.}0],[f(x),0\mathrm{.}60206,0\mathrm{.}65321,0\mathrm{.}74036,0\mathrm{.}77815]]$

Use a Matlab$/$Octave command to fit a polynomial that passes through them.

$[2]$

Write a Matlab$/$Octave program to approximate the value $f(4\mathrm{.}7),$ and $f(5\mathrm{.}7)$ using

a$)$ Lagrange interpolating polynomials of degree $3.$

b$)$ Newton's interpolating polynomials of degrees $3.$

c$)$ Write the error of each approximation. Which polynomial do you think gives a better approximation? Justify your answer.

$[3]$

using Octave please