I have to classify the point $(2,-4)$ for the function $f(x,y)=(x-2)^2-(y+4)^4$ which have a null hessian. What kind of point is (max/min)? Thanks
Classification of a point with null hessian
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analysis
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0If it were a local minimum, then $f$ would only take positive values near the point. And if it were a local maximum, then $f$ would only take negative values near the point. But in this case, it can't be either, because [...]. – 2012-03-29
1 Answers
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HINT : First of all $f(2,-4)=0$. Then $f(x,-4)\geq0$ and $f(2,y)\leq0$.
Therefore.....