# Thread: Volume of a rectangular box

1. ## 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.

2. Does anyone have any ideas for this problem? I am still having trouble with it.

3. Originally Posted by eigenvector11
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 $y\;\;\text{and}\;\;z$