(820,#45) 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

Solution:

If the volume is a maximum, :

Substituting into B),

Thus, the critical points are (6,0), (0,0), (0,3), (2,1)

Using the Second Derivative Test,

Therefore, produces the maximum volume.

Without computing the Second Derivative Test, we can still see that (2,1) is the maximum just by the geometry of the rectangular box.

Thus,

No Maple Code for this problem.

by:sh