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Math Help - volume of largest rectangular box

  1. #1
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    volume of largest rectangular box

    Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes, and one vertex in the plane . Largest volume is
    i have no idea how to get started. pls help.
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  2. #2
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    V = xyz = 36yz - 4y^2z -9yz^2
    V_{y} = 36z - 8yz -9z^2 = 0
    V_{z} = 36y - 4y^2 - 18yz =0

    then solve for y,z and i got

    y=0, z=0
    y=5/2, z = 16/9

    and substitude y and z into V and i got V = 400/9

    but it's not the right answer. anything wrong? Please help! due tonight
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