Find the dimensions of the largest rectangular box in the first octant of the xyz-coordinate system that has one vertex at the origin and the opposite vertex on the plane x + 2y + 3z = 6.
Added by Rhonda M.
Step 1
Given the plane equation x + 2y + 3z = 6, we can rewrite it as z = (6 - x - 2y)/3. So, the opposite vertex on the plane can be represented as (x, y, (6 - x - 2y)/3). Show more…
Show all steps
Close
Your feedback will help us improve your experience
Devendra Jangir and 99 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
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 $.
Partial Derivatives
Maximum and Minimum Values
Oswaldo J.
Find the maximum volume of a rectangular box with three faces in the coordinate planes and a vertex in the first octant on the plane $x+y+z=1$
PARTIAL DERIVATIVES
Maxima and Minima of Functions of Two Variables
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD