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October 2, 2014

Homework Help: Calculus

Posted by Isaac on Tuesday, August 9, 2011 at 11:25am.

A manufacturer constructs open boxes from sheets of cardboard that are 6 inches square by cutting small squares from the corners and folding up the sides. The Research and Development Department asks you to determine the size of the square that produces a box of greatest volume. Proceed as follows. Let x be the length of a side of the square to be cut and V be the volume of the resulting box. Show that V = x(6-2x)^2 (sketched it already.)

Are there any restrictions on the value of x? Explain.

Estimate the largest volume.

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