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Consider the function $f(x,y)=(x+y)^4$ and determine whether $f$ has a maximum, a minimum or neither at the point $(0,0)$.

I thought I needed to use the second partial derivative test but how would I go about showing the point is neither a minimum nor a maximum if the test is inconclusive?

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Hint: what can you say about the fourth power of any real number?

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    It's a maximum or minimum. The point$(0,0)$is a minimum2012-12-13
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$f(0, 0) = 0$

What other values can $f$ assume? For example, at $(1,1)$, $(-1, 1)$, etc.