Consider the table below: X 2.0 4.0 7.0 8.0 10.0 f(x) 1.5 4.5 7.3+A 3.4+A+B 6.5+B+C+D AB-CD: The first 2 and the last 2 digits of your school number. Apply 2 interpolation methods below for the given data above: 1. Lagrange interpolation method. Show all your detailed calculations. No program. 2. Cubic spline interpolation method. Write a program in C or C++ or C# or Python to solve this problem. For only cubic spline interpolation, plot (graph) the spline curve from x=2.0 to 10.0 with Ax=0.2 interval. If you cannot graph the data by your program you write, you can use Excel or Matlab or so for graphing. Prepare your homework as a technical report including all necessary explanations and mathematical expressions by using MS Word and its Equation Editor. Convert it to a PDF file and submit it through Google Classroom.