Use the given function and the given interval to complete parts a and b. f(x) = 2x3 - 45x2 + 300x on [4,11] a. Determine the absolute extreme values of f on the given interval when they exist. b. Use a graphing utility to confirm your conclusions. a. What is/are the absolute maximum/maxima of f on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The absolute maximum/maxima is/are atx=. (Use a comma to separate answers as needed. Type exact answers, using radicals as needed.) O B. There is no absolute maximum of f on the given interval. What is/are the absolute minimum/minima of f on the given interval? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The absolute minimum/minima is/are| at x = (Use a comma to separate answers as needed. Type exact answers, using radicals as needed.) O B. There is no absolute minimum of f on the given interval. b. Choose the correct answer below. O A. O B. O C. O D. -1100- 640- -500- 3200- -3200- 500- -640 1100-x 3 y = 3 - - 2x2 - 12x Find the inflection point(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The point(s) is/are (Type an ordered pair, using integers or fractions. Simplify your answer. Use a comma to separate answers as needed.) O B. There are no inflection points. Find each local maximum. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. There is one local maximum value of at x = (Simplify your answers. Type integers or fractions.) O B. There are two local maxima. In increasing order of x-value, the values are and at x = and x = , respectively. (Simplify your answers. Type integers or fractions.) O C. There are no local maxima.Find each local minimum. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. There is one local minimum value of at x = (Simplify your answers. Type integers or fractions.) O B. There are two local minima. In increasing order of x-value, the values are and at x = and x = , respectively. (Simplify your answers. Type integers or fractions.) O C. There are no local minima. Find the open interval(s) on which the function is differentiable and concave up. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interval(s) is/are (Simplify your answer. Use a comma to separate answers as needed. Type your answer in interval notation.) O B. The function is never concave up. Find the open interval(s) on which the function is differentiable and concave down. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interval(s) is/are (Simplify your answer. Use a comma to separate answers as needed. Type your answer in interval notation.) O B. The function is never concave down