In this question, you will sketch the graph of the cubic function below. f (x) = 213 - 12x2 - 270x The derivative of this function can be shown to equal f' (x) = 612 - 24x -270 This derivative can be factored as follows: f' (x) = 6(2+5) (x-9) The second derivative of the function is given by f" (x) = 12x - 24 (a) At what two values of x does the derivative of f(x) equal zero? (Enter the smaller solution in the first box and the larger solution in the second box.) Smaller solution : Larger solution : (b) Which of the following descriptions apply to the function f(x)? (Check all that apply.) Of(x) is decreasing on (-5,9) f(x) is increasing on (-oo,-5) O f(x) is increasing on (9,00) f(x) is decreasing on (9,00) f(x) is increasing on (-5,9) f(x) is decreasing on (-co,-5) (c) At what value of x does the second derivative of f(x) equal zero? x : (d) Which of the following descriptions apply to the function f(x)? (Check all that apply.) Of(x) is concave upwards on (2,00) f(x) is concave upwards on (-0o, 2) f(x) is concave downwards on (-co, 2) f(x) is concave downwards on (2,co) (e) What are the co-ordinates of the relative maximum point?f(x) is concave upwards on (2,00) f(x) is concave upwards on (-0o,2) Of(x) is concave downwards on (-co,2) Of(x) is concave downwards on (2,00) (e) What are the co-ordinates of the relative maximum point? (f) What are the co-ordinates of the relative minimum point? (g) What are the co-ordinates of the inflection point? ( (h) What is the y intercept of the function? y intercept : (i) Find the x intercepts of the function. (Enter these numbers in order, from the smallest to the largest.) Smallest x intercept : Middle x intercept : Largest x intercept