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Math Help - Volume of a rectangular box

  1. #1
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    Volume of a 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 x + 2y + 3z = 6.

    Thanks for the help.
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  2. #2
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    Does anyone have any ideas for this problem? I am still having trouble with it.
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  3. #3
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    Quote Originally Posted by eigenvector11 View Post
    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 x + 2y + 3z = 6.

    Thanks for the help.
    V = xyz = yz(6-2y-3z)

    Now calculate the partial derivatives V_y\;\;\; \text{and}\;\;\;V_z set them to zero and solve for y\;\;\text{and}\;\;z
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