It is possible when solving for the coefficients for a cubic spline that one of the i ’s turns out to a linear function (versus a full cubic). This exercise explores this situation. Suppose there are...

It is possible when solving for the coefficients for a cubic spline that one of the


_i
’s turns out to a linear function (versus a full cubic). This exercise explores this situation. Suppose there are three data points, with


₁

= 0,


₂

= 1, and

₃
= 2 and let

(a) To be a cubic spline it is required that

²(0, 2). What conditions must be imposed on the coefficients so this happens?

(b) Under what conditions, if any, is this a natural cubic spline?