Functional Analysis Question:

It is known that if a e ("[a, b] and y is the cubic spline corresponding to r and a partition Pr of [a, b] and satisfying y (t;) = = (t;) , y'(a) = ='(a), and y'(b) = I'(b), then we have Sex" (t ) ? dt > Say" (t ) ? dt A possible geometric interpretation is that a cubic spline function minimizes the integral of the square of the curvature, at least approximately. Explain