Let f = C [a, b] be given at equidistant points x; = a + ih, i = 0, 1, ... n, where nh = b a. Assume further that f'(a) (derivative at the left end point of the domain [a,b]) is given as well. Construct an algorithm for C piecewise quadratic interpolation of the given values. Hint: The process is similar to the cubic spline derivation. Here, the interpolating function on each subinterval is Si(2) = ai + b(x xi) + Ci (x xi), xi x Xi+1, for i = 0,...n - 1. Your job is to specify an algorithm for determining the 3n coefficients ai, bi, Ci.