Determine the intervals on which the given function is concave up or concave down and find the points of inflection. f(x) = (x – 14)(1 – x³) (Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the form (*, *). Enter DNE if there are no points of inflection.) points of inflection: (x, y) = (0,–14),(7,2394) (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", or "]", depending on whether the interval is open or closed. Enter Ø if the interval is empty.)

Find the open intervals where the function is concave upward or concave downward. Find any inflection points. AY 26 X AL Select the correct choice below and, if necessary, fill in the answer box(es) to complete your choice. OA. The function is concave upward on the interval(s) on the interval(s) (Type your answers in interval notation. Use a comma to separate answers as needed.) OB. The function is concave upward on the interval(s) concave downward. (Type your answer in interval notation. Use a comma to separate answers as needed.) and concave downward The function is never OC. The function is concave downward on the interval(s). The function is never concave upward. (Type your answer in interval notation. Use a comma to separate answers as needed.) OD. The function is never concave upward or downward. OA. The function has an inflection point at Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OB. The function does not have an…

Use the first derivative test and the second derivative test to determine where each function is increasing, decreasing, concave up, and concave down. 1 3 y = (4x-1) XER Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The function is increasing on (Type your answer in interval notation. Use integers or fractions for any numbers in the expression. Simplify your answer.) OB. The function is not increasing on any interval.