1a. Write down by hand the Lagrange interpolation polynomial for each of these sets of points. (Don't multiply out) (2,3), (3,5) (2,3), (3,5), (4.5,4) (2,3), (3,5), (4.5,4), (1,1) 1b. Find the Newton interpolation polynomial by hand for the sets of points in problem 1a, and write the result in Horner form. Do it the naive way, by solving successively for each coefficient to make it fit the next point. 1a. Write down by hand the Lagrange interpolation polynomial for each of these sets of points. (Don't multiply out) (2,3), (3,5) (2,3), (3,5), (4.5,4) (2,3), (3,5), (4.5,4), (1,1) 1b. Find the Newton interpolation polynomial by hand for the sets of points in problem 1a, and write the result in Horner form. Do it the naive way, by solving successively for each coefficient to make it fit the next point