Classification of a point with null hessian

Question

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

Hint: Just look at the function until you see the answer... (One term is nonnegative, the other is nonpositive.)
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.
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 [...].

Andrea Mori · Answer 1 · 2012-03-28 11:46:19Z

up vote 1 down vote

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

Therefore.....

answered Mar 28 '12 at 11:46

Andrea Mori
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