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## Homework Statement

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

## Homework 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)

## 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.