Use a given function $f(x)=270+141x-154x^2-12x^3+12x^4-x^5$ to generate a set of $N=10$ of equidistant

interpolation nodes $f(x_i)=y_i,i=1,$dots,$N$ in the range $-4,0.$

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 $6$ 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 $1).$

Case $2$: Repeat the same task for Chebyshev distribution of $N$ interpolation nodes and show the result

in Figure $2.$

Estimate the mean accuracy $\frac{1}{n-1}{\displaystyle \underset{j=1}{\overset{n-1}{}}}|f(x_j)-y_j|$ and maximum interpolation error max $|f(x_j)-y_j{|}_j=1^{n-1}$ in each

case. Print four values in the file 'results.txt$\text{'}$ with corresponding labels.

Create a pdf file Name$\_$task$1\_$nrN$.$pdf with the text of your code, Figure $1,$ Figure $2$ and four values

of the accuracy.