Write a function mfile that uses this formula to generate a set of data points. Your function should use those points along with the interpolation approaches outlined below to generate interpolated data $($x$\_$i$,$ f$\_$i$)$ on a specified increment. Your function should accept the following inputs $($in order$)$:

A vector of x values at which f$($x$)$ is to be evaluated to generate the sampled data.

A scalar input specifying the increment to use for the interpolated data.

Your function should use the following three approaches to generate interpolated data:

A polynomial of order $($N$-1)$ where N is the number of points in the sampled data

A linear spline

A clamped cubic spline with derivative end conditions set to values equal to the exact analytical derivative of f$($x$)$ evaluated at the end points.

Your function should have the following three outputs $($in order$)$:

The interpolated data $($f$\_$i$)$ generated with polynomial interpolation $($column vector$)$

The interpolated data $($f$\_$i$)$ generated with a linear spline $($column vector$)$

The interpolated data $($f$\_$i$)$ generated with the clamped cubic spline $($column vector$)$