(b) To determine the absolute extreme values of the function f, we need the critical numbers of f (c) To find these critical numbers, we need to find I' (x) . (Express your answer as a single fraction. Use positive exponents only.) (d) These critical numbers are as follows. (Enter your answers as a comma-separated list. If an answer does not exist enter DNE.) (e) The Closed Interval Optimal Test -Select-] be used to find the absolute maximum value and the absolute minimum value of the function. Submit Answer Viewing Saved Work Revert to Last Response DETAILS MY NOTES ASK YOUR TEACHI The average annual price of single-family homes in a county between 2000 and 2010 is approximated by the function P(t) = 0.32613 - 6.973t2 + 45.806t + 200 (0 s t s 10) where P(t) is measured in thousands of dollars and t is measured in years, with t = 0 corresponding to 2000. (a) When was the average annual price of single-family homes in the county highest? Round your answer to two decir places. years after 2000 (b) What was the highest average annual price during the period in question? Round your answer to three decimal places. thousand dollars Complete the following parts. (1) The domain of the function P is . (Enter your answer using interval notation.) (2) To answer the above questions, we need the critical numbers of P To find these critical numbers, we need to find P.(1) (4) These critical numbers are as follows. (Round your answer(s) to two decimal places. If a critical number is an endpoint of the domain, do NOT Include it in your answer. Enter your answers as a comma-separated list. If an answer not exist, enter DNE.) (5) The Closed Interval Optimal Test -Select-- ] be used to find the absolute extrema of the function. Submit Answer Viewing Saved Work Revert to Last Response CO DETAILS MY NOTES ASK YOUR TEACHI You construct an open box with locking tabs from a square piece of material, 20 inches on a side, by cutting equal squat from the corners and folding along the dashed lines (see figure, where M = 20). Determine the length of the side x of th equal square at each corner that will maximize the volume of the resulting box. M