Find the open interval(s) on which the function is increasing and decreasing. Identify the function's local and absolute extreme values, if any, saying where they occur. g(x) = X - 3x a. Determine the open interval(s) of x for which g(x) increases. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is increasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The function is never increasing Determine the open interval(s) of x for which g(x) decreases. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function is decreasing on the open interval(s) (Type your answer in interval notation. Use a comma to separate answers as needed.) O B. The function is never decreasing. b. Find each local maximum, if there are any. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. (Type integers or simplified fractions.) A. The function has a local maximum value at three values of x. In increasing order of x-value, the maximum values are g( ) = . g( ) - , and 9 ( D) -. B. The function has a local maximum value at two values of x. In increasing order of x-value, the maximum values are g ( ) = and g() - C. The function has a local maximum value at one value of x. The maximum value is g( ) O D. There are no local maxima