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.

Transcribed Image Text:

A(0) = 16 sin 0(cos 0 + 1) 0° < 0 < 90° 4 in → 4 in →-4 in – -12 in