Chapter 3.4, Problem 6CP

Find and plot the cubic spline $S$ satisfying

$S\left(0\right)=1$,

$S\left(1\right)=3$,

$S\left(2\right)=3$,

$S\left(3\right)=4$,

$S\left(4\right)=2$ and with

$S^{\prime }\left(0\right)=-2$

and $S^{\prime }\left(4\right)=1$.