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Math Help - setting up this equation (two variable one constraint)

  1. #1
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    setting up this equation (two variable one constraint)

    Find the max and min distance from the origin to the ellipse x^2+xy+y^2=3
    Use x^2+y^2 as your objective function.

    I tried to do this by using x^2+xy+y^2=3 as my constraint but it doesn't give me the right answer. I can't check the qualification of the constraint because there is an X and a Y when I take partial deriviative of that function. I don't know what to do..

    thanks alot
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  2. #2
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    Quote Originally Posted by s0urgrapes View Post
    Find the max and min distance from the origin to the ellipse x^2+xy+y^2=3
    Use x^2+y^2 as your objective function.

    I tried to do this by using x^2+xy+y^2=3 as my constraint but it doesn't give me the right answer. I can't check the qualification of the constraint because there is an X and a Y when I take partial deriviative of that function. I don't know what to do..

    thanks alot
    Your Lagrangian is:

    L(x,y,\lambda)=x^2+y^2+\lambda(x^2+xy+y^2-3)

    So now what is the problem?

    CB
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  3. #3
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    Quote Originally Posted by CaptainBlack View Post
    Your Lagrangian is:

    L(x,y,\lambda)=x^2+y^2+\lambda(x^2+xy+y^2-3)

    So now what is the problem?

    CB
    So to find the max and min of the function, I take the partial derivatives with respect to X, Y and lambda, then what? I get stuck after that

    Thanks!
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  4. #4
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    Quote Originally Posted by s0urgrapes View Post
    So to find the max and min of the function, I take the partial derivatives with respect to X, Y and lambda, then what? I get stuck after that

    Thanks!
    Equate the partial derivatives to zero and solve the resulting system of simultaneous equations.
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  5. #5
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    ok i got that, thanks!

    now theyre asking me to check the second order conditions for those partial derivatives..

    how do i do that?
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