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17 June, 00:21

You are constructing a cardboard box with the dimensions 4 m by 6 m. You then cut equal-size squares (x by x squares) from each corner so that you may fold the edges to get a box. How long should x be to get a box with the maximum volume? Round your answer to three decimal places. (enter numbers only)

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  1. 17 June, 01:21
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    0.785 m

    Step-by-step explanation:

    (4-2x) (6-2x) x = Volume

    Volume = 4x³ - 20x² + 24x

    Max volume: dV/dx = 0

    dV/dx = 12x² - 40x + 24 = 0

    3x² - 8x + 6 = 0

    x = 2.54858377, 0.784749563

    Max when d²V/dx² < 0

    d²V/dx² = 6x - 8

    At x = 0.784749563

    6x - 8 = - 3.29 < 0
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