a. Use Algorithm 3.2 to construct the interpolating polynomial of degree four for the unequally spaced points

Question:

a. Use Algorithm 3.2 to construct the interpolating polynomial of degree four for the unequally spaced points given in the following table:
x f (x)
0.0 −6.00000
0.1 −5.89483
0.3 −5.65014
0.6 −5.17788
1.0 −4.28172
b. Add f (1.1) = −3.99583 to the table, and construct the interpolating polynomial of degree five.