Assignment Curve$-$Fitting : Interpolation

Given the following dataset:

$\backslash$table$[[x,1,2,3,5,7,8],[f(x),3,6,19,99,291,444]]$

Calculate $f(4\mathrm{.}5)$ using:

a$.$ Newton's interpolating polynomial

b$.$ Lagrange's interpolating polynomial

For each $($a$)$ and $($b$)$ do polynomial interpolation order $1$ through $4.$ Choose your base points to attain good accuracy.

c$.$ What do your results indicate regarding the order of the polynomial used to generate the data in the table?

d$.$ Estimate the error for each order for $($a$)$ and $($b$)$ for each order $($from order $1$ though order $4)$

Make programming code to run in OCTAVE to solve problems no $1$ from point $($a$)$ to point $($d$).$