Write a program to compute the base functions one-by-one and the Lagrange polynomial. The output should show all the steps of the calculations. (JAVA Program) 1. a. f(0.25) if f(-1) 0.86199480, -0.5)-0.95802009, 40)-1.09861 23, f(0.5) 1.2943767 Write a program to implement the divided differences algorithm. The output must show the entire Newton triangle and all the steps of the extension for the higher degree a. Use Algorithm 3.2 to construct the interpolating polynomial of degree four for the unequally 2. spaced points given in the following table: xfCx) 0.0 -6.00000 0.1 -5.89483 0.3 |-5.65014 0.65.17788 1.0 |-4.28172 b. Add f ( 1.1 ) =3.99583 to the table, and construct the interpolating polynomial of degree five. Write a program to compute the base functions one-by-one and the Lagrange polynomial. The output should show all the steps of the calculations. (JAVA Program) 1. a. f(0.25) if f(-1) 0.86199480, -0.5)-0.95802009, 40)-1.09861 23, f(0.5) 1.2943767 Write a program to implement the divided differences algorithm. The output must show the entire Newton triangle and all the steps of the extension for the higher degree a. Use Algorithm 3.2 to construct the interpolating polynomial of degree four for the unequally 2. spaced points given in the following table: xfCx) 0.0 -6.00000 0.1 -5.89483 0.3 |-5.65014 0.65.17788 1.0 |-4.28172 b. Add f ( 1.1 ) =3.99583 to the table, and construct the interpolating polynomial of degree five