Pre-calculus

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum volume.

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  1. Volume = x(8-2x)(12-2x) , where 0 < x < 4
    = 96x -40x^2 + 4x^3
    d(volume)/dx = 96 - 80x + 12x^2
    = 0 for a max/min of volume
    3x^2 - 20x + 24 = 0

    use the quadratic formula to solve, reject the x value outside our stated domain above

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