Question

Problem 6: Interpolation, least squares, and finite difference Consider the following data table: 2 = 0 0.2 0.4 0.6 f(x) = 2 2.018 2.104 2.306 A cubic spline interpolation over these data is constructed as a cubic polynomial interpolating over all 4 data points. None of the above. is constructed by piece-wise locally cubic polynomial interpolation that maintains continuity of the first and second derivatives at the data points is constructed by plece-wise locally cubic polynomial interpolation that has discontinuous first and second derivatives at the data points.

Answer 1

3rd part is correct because after making the cubic splines the derivatives will be continuous as the difference between data points and respective values are coherent.