Use a given function $f(x)=x^3+3x^2-6x-8$ to generate a set of $N=20$ interpolation nodes $f(x_i)=y,$

$i=1,$dots,$12$ in the range $-5,0.$

Case $1$: construct at interpolation nodes $(x_i,y_i)$ of the Lagrange interpolation polynomial $P(x)$ and

compute values of $P(x)$ at points placed $3$ times denser than the selected set of the interpolation nodes.

Show the continuous function $f(x),$ interpolation nodes $(x_i,y_i)$ and Lagrange interpolation polynomials

$P(x)$ in one plot $($Figure $1)$ Can you write this code in C programming as a beginner?