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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?
     
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