Let f C3[a,b] be given at equidistant points xi = a + ih, i = 0,1,...,n where nh = b a. Assume further that f(a) is given as well.

Let f [a,b] be given at equidistant points xi-a + ih, i-0, 1, Assume further that f'(a) is given as wel. , n where nh-b-a (a) Construct an algorithm for Cl piecewise quadratic interpolation of the given values. Thus, the interpolating function is written as for0,...,n -1, and your job is to specify an algorithm for determining the 3n coeficients ai, b; and ci (b) How accurate do you expect this approximation to be as a function of h? Justify Let f [a,b] be given at equidistant points xi-a + ih, i-0, 1, Assume further that f'(a) is given as wel. , n where nh-b-a (a) Construct an algorithm for Cl piecewise quadratic interpolation of the given values. Thus, the interpolating function is written as for0,...,n -1, and your job is to specify an algorithm for determining the 3n coeficients ai, b; and ci (b) How accurate do you expect this approximation to be as a function of h? Justify