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Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.) f(x,y) =xy, 4x

Find the minimum and maximum values of the function subject to the given constraint. (If an answer does not exist, enter DNE.)

f(x,y) =xy, 4x²+16y²= 32

I keep getting my min being -4sqrt(2)/3 and my max being 4sqrt(2)/3, but apparently that's wrong. What's the correct answer and how do I get it?

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