Consider the function x) 2 241%: 8). This function has two critical points A

Consider the function f(x) Find A x x 8). This function has two critical points A < B and B Hint: Write the derivative in the form For each of the following intervals; tell whether f(x) is increasing (type in INC) or decreasing (type in DEC). [B, 00) The critical point A is a local (type in MAX, MIN or NEITHER) and the critical point B is a local (type in MIN or NEITHER) There are two numbers C < Dwhere either f = 0 or ) x is undefined. Find C and D Finally for each of the following intervals, tell whether f(x) is concave up (type in CU) or concave down (type in CD). (D, 00) A rectangular box is to be made from a piece of cardboard 20 inches long and 12 inches wide by cutting out identical squares from the four corners and turning up the sides; as in Figure 1 (Section 3_4, Example 1). Find the dimensions of the box of maximum volume. Length: inches, width: inches; height: inches What is this volume? cubic inches A farmer has 500 meters of wire fence with which he plans to build two identical adjacent pens; What is the maximum area of such an enclosure? square meter A right circular cylinder is inscribed in a right circular cone with altitude 10 and radius of the base 3. What is the greatest possible volume of the cylinder? The top and bottom margins of a poster are 2 cm and the side margins are each 8 cm_ If the area of printed material on the poster is fixed at 386 square centimeters, find the dimensions of the poster with the smallest area. Width Height The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 336 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 8 dollar increase In rent Similarly, one additional unit will be occupied for each 8 dollar decrease in rent. What rent should the manager charge to maximize revenue? Note: Revenue is the total amount of money brought in; in this problem it is equal to the rent per apartment times the number of apartments rented.