You construct an open-top box by cutting equal sized squares (x by x inches) out of the four corners of a 14 inch by 24 inch sheet of metal and then folding up the sides. Find a function for the volume of the box as a function of x and then determine the largest volume possible.

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You construct an open-top box by cutting equal sized squares (x by x inches) out of the four corners of a 14 inch by 24 inch sheet of metal and then folding up the sides. Find a function for the volume of the box as a function of x and then determine the largest volume possible.

Mathematics
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Volume Box = l*w*h l=24-2x w = 14-2x h = x (24-2x)(14-2x)(x) (24-2x)(14x-2x^2) 336x -48x^2 -28x^2 +4x^3 V = 4x^3 -76x^2 + 336x find the max vloume; get the derivative.. V' = 12x^2 -152x +336 v'=4(3x^2 -38x +84) find solve for V'=0 3x^2 -38x +84 = 0 38/6 +- sqrt(1444 - 1008)/6 19/3 +- sqrt(109)/3 x=9.8 or 2.85 is what I get if I didnt mess it up :)

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