For the following function, a) give the coordinates of any critical points and classify each point as a relative maximum, a K relative minimum, or neither; b) identify intervals where the function is increasing or decreasing; c) give the coordinates of any points of inflection; d) identify intervals where the function is concave up or concave down, and e) sketch the graph. g ( x) =x3 - 6x2+9x+ 1 a) What are the coordinates of the relative extrema? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The relative minimum point(s) is/are and the relative maximum point(s) is/are (Simplify your answers. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O B. The relative minimum point(s) is/are and there are no relative maximum point(s). 0 (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O C. The relative maximum point(s) is/are and there are no relative minimum point(s). (Simplify your answer. Use integers or fractions for any numbers in the expression. Type an ordered pair. Use a comma to separate answers as needed.) O D. There are no relative minimum points and there are no relative maximum points. b) On what interval(s) is g increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice.c) What are the coordinates of the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The coordinates of the inflection point(s) are (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) O B. There are no inflection points. 0d) On what interval(s) is g concave up or concave down? Select the correct choice below and fill in the answer box(es) to complete your choice. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O A. The function is concave up on and is never concave down. O B. The function is concave up on and concave down on O C. The function is concave down on and is never concave up. e) Choose the correct graph below. K O A. O B. O c. OD. X + Ay + My + + X 12 X -2b) On what interval(s) is g increasing or decreasing? Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function is increasing on The function is decreasing on (Simplify your answers. Type your answers in interval notation. Use a comma to separate answers as needed.) O B. The function is increasing on The function is never decreasing. 0 (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O C. The function is decreasing on The function is never increasing. (Simplify your answer. Type your answer in interval notation. Use a comma to separate answers as needed.) O D. The function is never increasing or decreasing