Exercise Solution 2.17
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
[s3]

[s4]

[s5]

[s6]

The second condition requires
[s7]
The third condition requires
[s8]
and the fourth condition requires
[s9]

[s10]

We have eight equations in eight unknowns. These can be expressed as
[s11]
which we solve to obtain
[s12]
Our two polynomials are
[s13]

[s14]
