Solve the problem.
-A piece of rectangular sheet metal is 21 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. Let x represent the length of each of the parallel sides. For what value of x will the area of
The cross section be a maximum (and thus maximize the amount of water that the gutter will hold)? If necessary,
Round to 2 decimal places.
A) 10.5
B) 5.25
C) 84
D) 42

Question

Quizplus · Accepted Answer

The area of the cross-section of the gutter, when the sides are turned up, can be represented as A = x(21 - 2x), where x is the height of the sides. To find the maximum area, we differentiate the area function with respect to x and set the derivative equal to zero. The derivative of A with respect to x is dA/dx = 21 - 4x. Setting this equal to zero gives 21 - 4x = 0, solving for x gives x = 5.25. This means the area of the cross-section is maximized when the height of the sides is 5.25 inches.

Solve the Problem. -A Piece of Rectangular Sheet Metal Is 21 Inches Wide