solve fully Question $4$: Lagrangian interpolation:

Suppose that we have the following data pairs$-x-$values and $f(x)-$values$-$ where $f(x)$ is some un$-$

known function:

Table $1$: Data for curve fitting

$(4\mathrm{.}1)$ Use the Lagrangian polynomial to interpolate the data in the table.

$(4\mathrm{.}2)$ Repeat the above question by using Mathematica commands. Give a command to generate

the whole interpolation. Present all commands and results generated.

$(4\mathrm{.}3)$ Give a single Mathematica command that uses Lagrangian polynomial to interpolate the data

in the table.

$(4\mathrm{.}4)$ Plot the points in the table using mathematica.

$(4\mathrm{.}5)$ Plot the interpolation polynomial you obtained using mathematica.