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Answer the following questions about the function whose derivative is f'(x) = (x - 2)(x + 7)(x - 6). a. What are the critical points of f? b. On what open intervals is f increasing or decreasing? c. At what points, if any, does f assume local maximum and minimum values? . . . a. Find the critical points, if any. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The critical point(s) of f is/are x = (Simplify your answer. Use a comma to separate answers as needed.) O B. The function f has no critical points.b. Determine where f is increasing and decreasing. Select the correct choice below and fill in the answer box to complete your choice. (Type your answer in interval notation. Use a comma to separate answers as needed.) O A. The function is increasing on the interval(s) and decreasing on the interval(s) O B. The function f is decreasing on the open interval(s) and never increasing. O C. The function f is increasing on the open interval(s) and never decreasing.c. List the points, if any, where f assumes a local maximum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. x= (Simplify your answer. Use a comma to separate answers as needed.) O B. There is no local maximum. List the points, if any, where f assumes a local minimum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OA. x= (Simplify your answer. Use a comma to separate answers as needed.) O B. There is no local minimum