$2-$ Under the title: "Splines vs Interpolation", write at most $3-$page $($small$)$ report about "Runge's phenomenon" explaining why splines were introduced to overcome interpolation problem described by this phenomenon.

To back up your report, it should include the python code and its resulting plot that produces the following plot $($a graph of the interpolation of the function $f(x)=\frac{1}{1+x^2},$ using lagrange's method, in the range $-4,4,$ using $15$ equispaced points, Notice that: Green: the resulting interpolation function, Blue: the original function, Orange: the points used in interpolation$).$ We recommend also that you provide the plot of the cubic spline of the above function $($in a separate graph$).$