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 off 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 at x= (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 off 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. OD. -1100- G40TY Ay -500- 3200- -3200 500- -640- 1100- 11 11Explain why if a runner completes a 6.2-mi race in 32 min, then he must have been running at exactly 11 mi/hr at least twice in the race. Assume the runner's speed at the finish line is zero. Select the correct choice below and, if necessary, fill in any answer box to complete your choice. (Round to one decimal place as needed.) O A. The average speed is mi/hr. By MVT, the speed was exactly mi/hr at least once. By the intermediate value theorem, all speeds between and mi/hr were reached. Because the initial and final speed was mi/hr, the speed of 11 mi/hr was reached at least twice in the race. O B. The average speed is mi/hr. By MVT, the speed was exactly mi/hr at least twice. By the intermediate value theorem, the speed between and mi/hr was constant. Therefore, the speed of 11 mi/hr was reached at least twice in the race. O C. The average speed is mi/hr. By the intermediate value theorem, the speed was exactly mi/hr at least twice. By MVT, all speeds between and mi/hr were reached. Because the initial and final speed was mi/hr, the speed of 11 mi/hr was reached at least twice in the race.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