Solve the problem
-A piece of rectangular sheet metal is 17 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) $8.5 \mathrm { in }$.
B) $4.25 \mathrm { in }$.
C) $68 \mathrm { in }$.
D) $34 \mathrm { in }$.

Question

Quizplus · Accepted Answer

The area $A$ of the cross-section of the gutter can be expressed as $A = x(17 - 2x)$, where $x$ is the height of the sides. To find the maximum area, we differentiate $A$ with respect to $x$ and set the derivative equal to zero. The derivative of $A$ with respect to $x$ is $A' = 17 - 4x$. Setting $A' = 0$ gives $17 - 4x = 0$, which solves to $x = 4.25$ inches. This is the value of $x$ that maximizes the cross-sectional area of the gutter.

Solve the Problem -A Piece of Rectangular Sheet Metal Is xxx

Solve the Problem
-A Piece of Rectangular Sheet Metal Is $x$