How do we handle the two ends of a piecewise cubic spline curve where there's not another derivative to match? Would it be possible to minimize the second derivative as well to obtain a "smoother" curve?
Can we replace matching two first-order derivatives with matching one first-order derivative and one second-order derivative? For certain situations, it might be an easier value to obtain.
What if the first derivative of an endpoint is infinite (a vertical tangent line). How do we plug it into the linear system solver?