# Second derivative test failure?

$f(x,y)=12x^2+12y^2+(x+y)^3$

Find all local maxima, minima and saddle points.

I found $2$ critical points $(0,0)$ and $(-2,-2)$ but the second derivative test came out weird for the set of points $(-2,-2)$. I got $f_{xx}=0$ and the discriminant bigger than $0$. That doesn't imply anything (not maxima, not minima, not saddle point and test isn't even inconclusive). What do I do at this point?

• Forgot that $f_{xy}$ was squared. Thank you! – Omrane Dec 14 '15 at 22:29