Use MATLAB to generate eight points from the function f(t) = sin 2 t from t = 0 to 2. Fit these data using (a)

Use MATLAB to generate eight points from the function f(t) = sin² t from t = 0 to 2π. Fit these data using

(a) Cubic spline with not-a-knot end conditions,

(b) Cubic spline with derivative end conditions equal to the exact values calculated with differentiation, and 

(c) Piecewise cubic hermite interpolation.
Develop plots of each fit as well as plots of the absolute error (E_t = approximation − true) for each.