Exercise Points$]$:

Consider the tabulated data

$\backslash$table$[[x,-7,-6,0,5],[y,-23,-12,-6,1]]$

a$)$ Derive the polynomial $p_l(x)$ in Lagrange form that interpolates the values $y$ at the nodes $x.$

b$)$ Use the polynomial and compute the interpolated value at $x=-1.$ Apply Aitken's algorithm and recompute the interpolated value.