A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, this length is bent up at an angle θ. See the illustration. The area A of the opening as a function of is given by
(a) In calculus, you will be asked to find the angle θ that maximizes A by solving the equation
(b) What is the maximum area A of the opening?
(c) Graph A = A(θ), 0° ≤ θ ≤ 90°, and find the angle θ that maximizes the area A. Also find the maximum area. Compare the results to the answer found earlier.
