Determine the natural cubic spline that interpolates the dat

Determine the natural cubic spline that interpolates the data f(0)=1, f(1)=3,
and f(2)=4, and then use the spline to determine f(0.5) and f(1.5). Please express your
results to 3 decimal places.

Solution

C ubic spline is f= -0.1667x³+2.1667x+1;

f(0.5)=2.0625 and f(1.5)=3.6875;