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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

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Hint: Just look at the function until you see the answer... (One term is nonnegative, the other is nonpositive.) –  Hans Lundmark Mar 28 '12 at 10:24
    
i don't know what are the consideration to do :(! i know that if the second term is positive then (2,-4) is a minimum. –  Math81 Mar 28 '12 at 10:32
    
If 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 [...]. –  Hans Lundmark Mar 29 '12 at 11:56

1 Answer 1

HINT : First of all $f(2,-4)=0$. Then $f(x,-4)\geq0$ and $f(2,y)\leq0$.

Therefore.....

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