Interpolate a cubic spline between the three points (0, 1), (2, 2), and (4, 0).

We seek to fit a cubic polynomial on the interval [0, 2] and another cubic polynomial on the interval [2, 4]. These take forms:

	[s1]
	[s2]

These must satisfy conditions [2.113] to [2.116]. The first condition requires that

The second condition requires

The third condition requires

and the fourth condition requires

We have eight equations in eight unknowns. These can be expressed as

which we solve to obtain

Accordingly, our two polynomials are

	[s13]
	[s14]