PROBLEM 1 (3 pts): Using divided difference algorithm, construct polynomial that interpolates the following data: f(0) = 2, f(1) = 4, f(3) = 2, and f(4) = 6. Write the polynomial in the Newton's form, and next, in the Newton's nested multiplica- tion form. PROBLEM 1 (4 pts): The function f(0) = cos(272) for 2 (0,1) is approximated by a a polynomial Pn interpolating f at n +1 points Ii. How should n be chosen so that the error max, f() - Pn(2)