Given 2 data set in the file duck.txt, I need to construct a code for cubic splines in python WITHOUT Scipy, only numpy. Thank you!

Cubic Splines. Construct cubic splines for the same data and plot the resulting approximation. Use the natural splines with free boundary conditions, i.e., the second derivatives of the constructed func tion must vanish at the end points. The outline below contains some of the theory behind the cubic spline approximation, however it does not have the two equations coming from the vanishing second derivative condition at the end points, xi and xv. Part of your task is to carry out this derivation on your own. Cubic Splines. Construct cubic splines for the same data and plot the resulting approximation. Use the natural splines with free boundary conditions, i.e., the second derivatives of the constructed func tion must vanish at the end points. The outline below contains some of the theory behind the cubic spline approximation, however it does not have the two equations coming from the vanishing second derivative condition at the end points, xi and xv. Part of your task is to carry out this derivation on your own