$($a$)$ Derive the cubic shape functions by using the Lagrange interpolati

$($b$)$ Assuming that $\backslash ($ L$=3\backslash )$ and $\backslash ($ a$=0\backslash ),$ plot the shape functions.

rigure $4\mathrm{.}50$ A $4-$noge element

Assuming that $\backslash ($ L$=3,$ a$=0\backslash )$ and the nodal values are $3\mathrm{.}0,5\mathrm{.}0,1\mathrm{.}0$ and $2\mathrm{.}0$ for nodes $\backslash (1,2,3\backslash ),$ and $4,$ respectively, calculate the interpolating cubic polynomial by using both the monomial basis and the Lagrange basis. Plot