Problem $4$:

$\backslash$table$[[$x$,0,1,2\mathrm{.}5,3],[$y$,2,5\mathrm{.}4375,7\mathrm{.}3516,7\mathrm{.}5625]]$

Use Lagrange interpolating polynomial to determine y at $x=1\mathrm{.}5$ to the best possible accuracy.

Deliverables $($Hand calculation, use MATLAB to simplify your equation$)$:

Order the data points centered around and as close as possible to the unknown.

Determine the Lagrange polynomial interpolation function of order $1($Linear$),$ Order $2($Quadratic$)$ and Order $3($Cubic$).$

Calculate $f(1\mathrm{.}5)$ using Linear, Quadratic and Cubic interpolation functions.