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A 33 by 33 square piece of cardboard is to be made into a box by cutting out equal square corners from each side of the square. What size corners should be cut out so that the volume of the box is maximized?

  • calculus -

    let x be cut size. sides are thus 33-2x

    v = x(33-2x)^2
    v = 4x^3 - 132x^2 + 1089x

    dv/dx = 12x^2 - 264x + 1089

    max/min volume when dv/dx = 0
    (2x-11)(2x-33) = 0

    I'll let you figure out which root makes sense.

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