10. Form the Hermite polynomial (with n=3) for f(I) between the values of x = 1 and 5 (a) (10 pts) Fill in the Divided Difference table below, as well as give your approximation at the bottom. Illustrate the calculation in the table indi- cated by a * and ** in the white space to the right of the table and keep the rest of the work on scratch paper. f(x) 1 3 5 f(a) f() 6 14.7 168 204.6 1260 1065.5 *** (b) (10 pts) What is H3(c)? (c) (5 pts) Approximate the value of f(2) using the Hermite polynomial. (You don't have to write the same thing as above. Just write the predicted answer.) H (2) = (d) (5 pts) Use the theory from the book to compute the bound on the error on this approximation. The true value of f(2) is 42. Compute the actual error. 10. Form the Hermite polynomial (with n=3) for f(I) between the values of x = 1 and 5 (a) (10 pts) Fill in the Divided Difference table below, as well as give your approximation at the bottom. Illustrate the calculation in the table indi- cated by a * and ** in the white space to the right of the table and keep the rest of the work on scratch paper. f(x) 1 3 5 f(a) f() 6 14.7 168 204.6 1260 1065.5 *** (b) (10 pts) What is H3(c)? (c) (5 pts) Approximate the value of f(2) using the Hermite polynomial. (You don't have to write the same thing as above. Just write the predicted answer.) H (2) = (d) (5 pts) Use the theory from the book to compute the bound on the error on this approximation. The true value of f(2) is 42. Compute the actual error