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(a)

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Express the volume $\"\"$ of the box as a function of the length $\"\"$ of the side of the square cut from each corner.

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Formula for the volume of the cubic box is $\"\"$ , where $\"\"$ is length, $\"\"$ is width and $\"\"$ is height.

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Observe the figure,

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Length of the box is $\"\"$ .

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Width of the box is $\"\"$ .

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Height of the box out is $\"\"$ .

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$\"\"$

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$\"\"$ .

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(b)

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Find the volume if the $\"\"$ -inch square is cut out.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Volume is $\"\"$ cubic inches.

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(c)

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Find the volume if the $\"\"$ -inch square is cut out.

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Volume is $\"\"$ cubic inches.

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(d) Graph the function $\"\"$ .

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$\"\"$

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Locate the minimum point on the graph.

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$\"\"$

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$\"\"$ is largest when $\"\"$ .

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(a) $\"\"$ .

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(b) $\"\"$ cubic inches.

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(c) $\"\"$ cubic inches.

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(d) Graph of the function $\"\"$ :

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$\"\"$

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$\"\"$ is largest when $\"\"$ .