(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I am trying to find the min and max values of f(x,y)=2x^2 + 3y^2 subject to xy=5.

2. Relevant equations

f(x,y)=2x^2 + 3y^2 subject to xy=5

[itex]\mathbf\nabla[/itex]f=(4x, 6y)

[itex]\mathbf\nabla[/itex]g=(y,x)

3. The attempt at a solution

When I go through the calculations, I end up with two critical points, but both yield the same maximum value. Is this correct that there are two maxs and no min? I'm skeptical. Any suggestions are appreciated.

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# Homework Help: Lagrange Multipliers: Minimum and Maximum Values

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