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Please Help!! What is the maximum possible volume for a rectangular box (with square base and no top) made from 12 square feet of cardboard?
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You know that area is \(12=4xy+x^2,\) and that volume is \(V=x^2y.\) Using the first equation, write an expression for either (1) x in terms of y, or (2) y in terms of x. Then, substitute that expression into the volume equation appropriately, and find the critical points of V(x) or V(y), depending on the sub you make.
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