2. Data interpolation has many applications. Suppose we have been given the task of finding the degree 3 polynomial P(x) = ar3 + bx2 + cx + d which satisfies P'(-1) = 3 and passes through the points (-1, 1), (0, 1), and (1, 3). (a) (3 points) Show that the coefficients of P satisfy the system of equations 3a - 2b + c = 3 -atb-c+d=1 d =1 atb+c+d=3. Then use the information above to write a matrix equation of the form A = r so we could solve for a, b, c, and d. (b) (5 points) Find A-, and use it to find a, b, c, and d. Write the formula for P(x). (c) (2 points) Your boss suddenly changes the problem at the last minute. You have now been asked to find the degree 3 polynomial f which satisfies 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