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.
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.
$\displaystyle V = xyz = yz(6-2y-3z)$
Now calculate the partial derivatives $\displaystyle V_y\;\;\; \text{and}\;\;\;V_z$ set them to zero and solve for $\displaystyle y\;\;\text{and}\;\;z$