Solve the Problem $x$ ,
B What Value Of Trough $x$ Will Maximize the Volume of Water That Can Be Carried

question 188

Multiple Choice

Solve the problem.
-A trough at the end of a gutter spout is meant to direct water away from a house. The homeowner makes the trough from a rectangular piece of aluminum that is 24 in. long and 8 in. wide. He makes
A fold along the two long sides a distance of x inches from the edge.
a. Write a function to represent the volume in terms of $x$ ,
b. What value of $x$ will maximize the volume of water that can be carried by the gutter?

• A) a. \(V ( x ) = - 2 x ^ { 2 } + 8 x ;\) b. \(x = 2\)
• B) a. \(V ( x ) = - 2 x ^ { 2 } + 8 x ;\) b. \(x = 1\)
• C) a. \(V ( x ) = - 48 x ^ { 2 } + 192 x\); b. \(x = 2\)
• D) a. \(V ( x ) = - 48 x ^ { 2 } + 192 x\); b. \(x = 1\)

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