9. [10 points) Given the function y = f(x) = -3x4 + 4x3 +1 (a) Plot the inction. (b) Find the derivative f '(x). (c) Plot f '(X). (d) What are the critical numbers of f(x)'? Use your plot. (e) Find the 2\"Cl derivative f ' '(x), (f) Plot f \"(x). (g) Use the 2\"Cl derivative test to determine if the critical numbers you found are relative/absolute maxima, relative/absolute minima, or neither of f(x), i.e. nd f \"(c) and determine what it tells you about the shape of the mction at x = c. (h) Do your computed 2"'1 derivative test results match your plot of f(x)? (yes or no) (i) Are there any points of inection? (yes or no)' If yes, what is x for a point of inection