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anonymous
 5 years ago
You construct an opentop 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.
anonymous
 5 years ago
You construct an opentop 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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amistre64
 5 years ago
Best ResponseYou've already chosen the best response.0Volume Box = l*w*h l=242x w = 142x h = x (242x)(142x)(x) (242x)(14x2x^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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