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Consider the function $f(x,y) = x^2 + xy + y^2$ defined on the unit disc $D = \{(x,y) \mid x^2 + y^2 \leq 1\}$.

I can not simplify the equations to the point where I find a constant for the lagrange multiplier and thus can't find the points of the extrema. I used the method that we can create a new function $L$ with the variables $x$, $y$ and $\lambda$ where $\lambda$ is the Lagrange multiplier. Then found the partials of $L$ with respect to each variable. This is where I am stuck because I can not simplify enough to find $x$ and $y$. Are there any tricks for this type of question?

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    Are you finding all extrema (mins and maxes) or just mins...?2012-12-02
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    I am finding both, but I actually solved the question. Thanks for commenting though2012-12-02

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