Solve the problem.
-A piece of rectangular sheet metal is 5 inches wide. It is to be made into a rain gutter by turning up equal edges to form parallel sides. If the length of each parallel side is x inches, what value of x will maximize the rain
Gutter's cross-sectional area (and thus maximize the amount of water the gutter will hold)? If necessary, round
To the nearest hundredth.
A) 1.25 in.
B) 10 in.
C) 20 in.
D) 2.5 in.

Question

Quizplus · Accepted Answer

The cross-sectional area of the rain gutter, when the sides are turned up, forms a rectangle with a width of (5 - 2x) inches (since both sides are turned up by x inches) and a height of x inches. The area, A, can be expressed as A = x(5 - 2x). To find the value of x that maximizes the area, we can take the derivative of A with respect to x, set it to zero, and solve for x. The derivative of A with respect to x is dA/dx = 5 - 4x. Setting this equal to zero gives 5 - 4x = 0, or x = 5/4 inches, which is 1.25 inches.

Solve the Problem. -A Piece of Rectangular Sheet Metal Is 5 Inches Wide