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Mean Value Theorem and Maximizing Volume of an Open Box

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The width of an open box is half its height and its surface area is 75 cm3. Find the dimensions to maximize its volume.

Indicate which of the following functions satisfies the conditions of the mean value theorem on the given interval.

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The Mean Value Theorem and Maximizing Volume of an Open Box are investigated. The solution is detailed and well presented.

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Solution

Let the dimension of box be .
From the question, we have and surface area is . (1)
The volume of the box is ...

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