The function f is continuous for all real numbers and the graphs of f' and f" are given. (-3 v/3.th) (30) (@) Determine the critical numbers of f. (Use symbolic notation and fractions where needed. Enter DNE if the solution does not exist. Give your answer in the form of a comma-separated list of numbers.) critical numbers: (b) Where is f increasing? (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (#, #). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter , if the interval is empty.) is increasing on (c) Where is f decreasing? (Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, #). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter 3 if the interval is empty.) f is decreasing on (d) At what numbers x, if any, does f have a local minimum? (Use symbolic notation and fractions where needed. Enter DNE if the solution does not exist. Give your answer in the form of a comma-separated list of numbers.)local minimum at the number(s): e) At what numbers x, if any, does f have a local maximum? Use symbolic notation and fractions where needed. Enter DNE if the solution does not exist. Give your answer in the form of a comma-separated list of numbers.) local maximum at the number(s): f) Where is f concave up? Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, #). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter @ if the interval is empty.) f is concave up on @) Where is f concave down? Use symbolic notation and fractions where needed. Give your answers as intervals in the form (*, *). Use the symbol co for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[" or "]" depending on whether the interval is open or closed. Enter @ if the interval is empty.) f is concave down on h) List the x-coordinates of any inflection points. (Use symbolic notation and fractions where needed. Enter DNE if the solution does not exist. Give your answer in the form of a comma-separated list of numbers.) inflection points at the number(s)