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 = 9.

The volume of largest rectangular box is 4.5 units.

Step-by-step explanation:

Since we have given that

Volume =

with subject to

So, let

So, Volume becomes,

Partially derivative wrt x and y we get that

By solving these two equations, we get that

So,

So, Volume of largest rectangular box would be

Hence, the volume of largest rectangular box is 4.5 units.

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