11. Please solve each part to this question and label each section in your work so I can easily understand which part your work goes with. Thank you!
Complete parts (a) through (c) for the following function. f ( x ) = x - 24x + 80 (a) Find intervals where the function is increasing or decreasing, and determine any relative extrema. (b) Find intervals where the function is concave upward or concave downward, and determine any inflection points. (c) Graph the function, considering the domain, critical points, symmetry, relative extrema, regions where the function is increasing or decreasing, inflection points, regions where the function is concave upward or concave downward, intercepts where possible, and asymptotes where applicable. (a) Find intervals where the function is 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 decreasing on and increasing nowhere. Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) O B. The function is increasing on and decreasing nowhere. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) C. The function is increasing on and decreasing on Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed. Type your answers in interval notation.) D. The function does not increase or decrease on any interval. Determine any relative extrema. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. O A. The function has a relative maximum at and a relative minimum at (Use a comma to separate answers as needed. Type ordered pairs.) B. The function has a relative minimum at but does not have any relative maxima. (Use a comma to separate answers as needed. Type an ordered pair.) O C. The function has a relative maximum at , but does not have any relative minima. (Use a comma to separate answers as needed. Type an ordered pair.) D. The function does not have any relative extrema. (b) Find intervals where the function is concave upward or concave downward. Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. A. The function is concave upward on , but is never concave downward. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) B. The function is concave downward on , but is never concave upward. (Simplify your answer, including any radicals. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed. Type your answer in interval notation.) C. The function is concave upward on and concave downward on (Simplify your answers, including any radicals. Use integers or fractions for any numbers in the expressions. Use a comma to separate answers as needed. Type your answers in interval notation.) O D. The function is neither concave upward nor concave downward on any interval. Determine any inflection points. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The function has an inflection point at (Use a comma to separate answers as needed. Type an ordered pair.) O B. The function does not have any inflection points. c) Choose the graph of the function. OA OB. O C. OD
