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Lagrange Multipliers (Multivariable Calc)

  1. May 6, 2007 #1
    1. The problem statement, all variables and given/known data
    Find the maximum x1, x2, x3, in the ellipsoid
    x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1 and all the places where this value is attained.

    2. Relevant equations

    3. The attempt at a solution
    My teacher said to use the lagrange multiplier.
    So far, I have that we are maximizing x1, x2, and x3 such that x1^2/a^2 + x2^2/b^2 + x3^2/c^2 < 1.

    In any case, I figured that the constraint would be the equation for the ellipsoid, but I haven't a clue what exactly we would be maximizing for.
    I would assume the maximum of x1,x2, and x3 would simply be the norm of the vector created by the three values.
    Last edited: May 7, 2007
  2. jcsd
  3. May 7, 2007 #2


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    Homework Helper
    Gold Member

    You need to show your work before you get help. What have you done with this problem?
  4. May 7, 2007 #3
    yeah I added what I did, but I feel like I'm going in the wrong direction.
  5. May 7, 2007 #4


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    Staff Emeritus
    Science Advisor

    I wouldn't. I accept exactly what was said here: that you are asked to find three separate values: the maximum value of x, the maximum value of y, and the maximum value of z- and you don't need "Lagrange multiplier", you can read them off the equation of the ellipsoid. If you think your teacher means anything else, you should ask him or her.
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