In this problem the data are: ( 1 , 1 ) = (0, 0), ( 2 , 2 ) = (1, 1), and ( 3 , 3 ) = (2, 3). (a) Find the global interpolation polynomial that fits these data. (b) Find the piecewise linear...

In this problem the data are: (
₁,

₁) = (0, 0), (
₂,

₂) = (1, 1), and (
₃,

₃) = (2, 3).

(a) Find the global interpolation polynomial that fits these data.

(b) Find the piecewise linear interpolation function that fits these data.

(c) Find the natural cubic spline that fits these data.