Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this way.

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  1. v = x(3-2x)(4-2x)
    dv/dx = 4(3x^2 - 7x + 3)
    dv/dx=0 when x = (7-√13)/6 = 0.566

    v = 3.03

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