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I'm slightly confused by a certain step I'm at in the homework. I have looked for extrema in the whole unrestricted function, and found them without much difficulty, but for finding the extrema of the "edges" of the constrained area, I'm not sure how to apply our technique. By setting $\nabla f = \lambda \nabla g$, I get the two equations we need, but the third "equation" is actually the inequality we were provided with as a constraint. Can we use this inequality to solve for $x$ and $y$, or is there another method that I'm missing?

I'm slightly confused by a certain step I'm at in the homework. I have looked for extrema in the whole unrestricted function, and found them without much difficulty, but for finding the extrema of the "edges" of the constrained area, I'm not sure how to apply our technique. By setting $\nabla f = \lambda \nabla g$, I get the two equations we need, but the third "equation" is actually the inequality we were provided with as a constraint. Can we use this inequality to solve for $x$ and $y$, or is there another method that I'm missing?

I'm slightly confused by a certain step I'm at in the homework. I have looked for extrema in the whole unrestricted function, and found them without much difficulty, but for finding the extrema of the "edges" of the constrained area, I'm not sure how to apply our technique. By setting $\nabla f = \lambda \nabla g$, I get the two equations we need, but the third "equation" is actually the inequality we were provided with as a constraint. Can we use this inequality to solve for $x$ and $y$, or is there another method that I'm missing?