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A rectangular prism is drawn in the first octant so that the lower left corner of its front face is at the origin and the

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A rectangular prism is drawn in the first octant so that the lower left corner of its front face is at the origin and the upper right corner of its back face is at a point P (x,y,z) . Find the maximum volume that the rectangular prism can have if the distance from the lower left corner of its front face to the upper right corner of its back face is 2M. 4

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