Sketch the graph of the following function. List the coordinates of where extrema or points of inflection occur. State where the function is increasing or decreasing as well as where it is concave up or concave down. f(x) = - x3 +9x2 - 54 . . . What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The coordinates of the relative extrema are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. There are no relative extrema. What are the coordinates of the inflection points? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The coordinates of the inflection points are (Simplify your answer. Type an ordered pair. Type an exact answer using radicals as needed. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. There are no inflection points.On what interval(s) is f increasing or decreasing? O A. f is increasing on (3,co). f is decreasing on ( - co, 3). O B. f is increasing on ( - co,3). f is decreasing on (3,co). C. f is increasing on ( - co,0) and (6,co). f is decreasing on (0,6). O D. f is never increasing. f is decreasing on ( - co, co). O E. f is increasing on ( - co,co). f is never decreasing. O F. f is increasing on (0,6). f is decreasing on ( - co,0) and (6,co). On what interval(s) is f concave up or concave down? O A. f is concave up on ( - co,3). f is concave down on (3,co). O B. f is concave up on (3,co). f is concave down on ( - co, 3). O C. f is concave up on ( - co,3) and (3,co). f is never concave down. O D. f is concave up (0,6). f is concave down on ( - co,0) and (6,co). O E. f is concave up on ( - co,0) and (6,co). f is concave down on (0,6). O F. f is never concave up. f is concave down on ( - co,3) and (3,co).