Somebody please help me to obtain piece-wise interpolating polynomials for the function $f(x)$ defined by the below data:
$x=1$, $f(x)=3$; $x=2, f(x)=3$; $x=4, f(x)=21$; $x=8, f(x)=73$
I know the polynomial is given by $p_1i= f_i-1 +(x-x_i-1 )f(x_i-1 ,x_i)$.