a. Find the open intervals on which the function is increasing and those on which it is decreasing. b. Identify the function's local extreme values, if any, saying where they occur. 14. x3 f(x)= 2x1 a. On what open interval(s), if any, is the function increasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function f is increasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function f is not increasing anywhere. On what open interval(s), if any, is the function decreasing? Select the correct choice below and, if necessary, fill in the answer box to complete your choice O A. The function f is decreasing on the interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) B. The function f is not decreasing anywhere. b. Find each local maximum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The function has (a) local maximum/maxima at the point(s) (Type an ordered pair. Use comma to separate answers as needed.) O B. There is no local maximum Find each local minimum, if any. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice A. The function has (a) local minimum/minima at the point(s) (Type an ordered pair. Use comma to separate answers as needed.) B. There is no local minimum.