Consider the table below: 1.0 2.0 3.0 4.05.0 f(x) 8.5 7.5 6.5 7.5 11.5 18.5 6.0 a) Obtain a polynomial fitting on these data points by using Lagrange interpolation method. Show all your detailed calculations b) Write a program in C or C++ or C# to solve this problem. c) Graph the data points as well as the polynomial with 5 extra points between each pairs (sequential polynomial points are connected with lines)