The following five points
(0, 1), (1, 7), (2, 27) (3, 79), (4, 181)
lie on a single cubic curve.
(a) Which of the three types of cubic splines (natural, parabolic runout, or cubic runout) would agree exactly with the single cubic curve on which the five points lie?
(b) Determine the cubic spline you chose in part (a), and verify that it is a single cubic curve that interpolates the five points.