The given function is g(x) = sin ( /2 x), and a cubic spline that interpolates this function at three nodes: x = 0, 1, and 2, using two cubic functions of the form

f1(x) = a1+b1x+c1x2+d1x3, for0x<1

f2(x) = a2+b2(x1)+c2(x1)2+d2(x1)3, for1x2.

solve for any coefficients that may be easily solved for; and for the others, arrive at a system of five equations that (in theory) could be solved given time, patience, or software. Make the spline clamped so that the derivative at x = 0 and 2 matches that of g(x)