Concept explainers
Constructing a Rain Gutter A rain gutter is to be constructed of aluminum sheets 12 inches wide. After marking off a length of 4 inches from each edge, the builder bends this length up at an angle . See the illustration. The area of the opening as a function of is given by
,
(a) In calculus, you will be asked to find the angle that maximizes A by solving the equation
Solve this equation for .
(b) What is the maximum area of the opening?
(c) Graph and find the angle that maximizes the area . Also find the maximum area.

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