Find the volume using partial differentiation. See my question at additional details.?

Question

Find the volume of the largest rectangular parallelepiped that has 3 faces in the coordinate planes and one vertex in the plane x+2y+3z=4

Answer 1

the volume is xyz such that x+2y+3z = 4

V = xyz

V = (4 - 2y - 3z)yz

= 4yz - 2y^2z - 3yz^2

.. . .

∂V/∂y = 4z - 4yz - 3z^2 = 0

∂V/∂z = 4y - 2y^2 - 6yz = 0

solving simultaneously .. . .. .

and we dont want the cases where y or z are zeros

y = 2/3

z = 4/9

thus

x = 12/9