2. Data interpolation has many applications. Suppose we have been given the task of nding the degree 3 polynomial 13(3) = ar3+bzr2+cm+d which satises P'(1) = 3 and passes through the points (1,1), (0, 1), and (1,3). (a) (3 points) Show that the coefcients of P satisfy the System of equations 30. 2b + c = 3 a+bc+d=1 d=1 a+b+c+d=3. Then use the information above to write a matrix equation of the form A = r so we could 9.0 c-EJ solve for a, b, c, and d. (b) [5 points) Find 111, and use it to nd n,b,c, and d. Write the formula for 19(3). (c) (2 points) Your boss Suddenly changes the problem at the last minute. You have now been asked to nd the degree 3 polynomial f which satises f'(1) = 13 and passes through the points (1,3), [0, 2), and (1,3). Use your work from parts (a) through (b) to find the formula for f