2. Develop cubic splines for the data below and

(a) predict f(4) and f(2.5),

(b) verify that f2(3) and f3(3) = 19, and

(c) plot your interpolant using Matlab (note you can create your xgrid as usual, but you will have to define the corresponding ygrid in pieces).

x 1 2 3 5 7 8

f(x) 3 6 19 99 291 444