Write down in details the formulae of the Lagrange and Newton's form of the polynomial that interpolates the set of data points (-20.yo), (21,41),..., (nyn). (3) 1-2. Use the results in 1-1. to determine the Lagrange and Newton's form of the polynomial that interpolates the data set (0,2), (1,5) and (2, 12). [18] 1-3. If an extra point say (4.9) is to be added to the above data set, which of the two forms in 1-1. would be more efficient and why? (Don't compute the corresponding polynomials.] [5]