1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Maximum value problem

  1. Jun 5, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the volume of the largest rectangular box with faces parallel to the coordinate planes that can be inscribed inside the ellipsoid :

    (x^2/a^2)+(y^2/b^2)+(z^2/c^2) = 1

    2. Relevant equations

    Volume of a rectangular box = x * y * z
    critical point formula.

    3. The attempt at a solution

    The volume of a box is maximised when x = y = z ?
  2. jcsd
  3. Jun 7, 2010 #2
    Not quite. Try rewriting x in terms of y and z and plugging this into your volume formula. This must hold since x is determined by y and z (i.e. the vertices of the rectangular box will lie on the ellipsoid.)

    Now, how do you find the maximum of a function of one variable? How do you find the maximum of a function of two variables?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook