A rectangle is constructed under the graph of f(x) =2m4 with the right lower corner at ( 6, 0) and one corner on the graph of f(x) = 2m4 (05x56). Represent the area A of the rectangle as a Note: Use " to raise x to a power (like x"3 for x cubed). What value of x will maximize the area of the rectangle? (Use your calculator or a graphing application to determine this. DO NOT USE CALCULUS.) Maximum area when x=[:] Note: Input the x value as a decimal number rounded to two decimal places (like 34.12 or 4.67) A rectangle is inscribed with its base on the x-axis and its upper corners on the semicircle defined by m2 + y2 = 36 in Quadrants | and II. What is the height of the rectangle with greatest possible area? A rectangle is constructed under the graph of f(x) =16 m2 with two corners on the x-axis and two corners on the graph of f(x) = 16 9:2 . Represent the area A of the rectangle as a Note: use " to raise x to a power (like x"2 for x squared). What value of x will maximize the area of the rectangle? Maximum area when X=:] Note: Input the x value as a decimal number rounded to two decimal places (like 34.12 or 4.67) 0.41% The concentration of a drug 1': hours after being injected is given by C(t) = . Find the time when t2 + 15 the concentration is at a maximum. Give your answer accurate to at least 2 decimal places. [3 hours. You have a wire that is 65 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum? The circumference of the circle is C] cm. Give your answer to two decimal places Suppose the Sunglasses Hut Company has a profit function given by P(q) = 0.01:;2 + 5q 47, where q is the number of thousands of pairs of sunglasses sold and produced, and P(q) is the total profit, in thousands of dollars, from selling and producing q pairs of sunglasses. A) How many pairs of sunglasses (in thousands) should be sold to maximize profits? (If necessary, round your answer to three decimal places.) Answer: I: thousand pairs of sunglasses need to be sold. B) What are the actual maximum profits (in thousands) that can be expected? (If necessary, round your answer to three decimal places.) Answer: I: thousand dollars of maximum profits can be expected