Let $f(x,y)=4x^2+4y^2+x^3y+xy^3-xy-4$
I found out that the critical points of the function are $(0,0),(1.5,-1.5)$ and $(-1.5,1.5)$. $f_{xx}=8+6xy$; $f_{yy}=8+6xy$; $f_{xy}=3x^2+3y^2-1$. $f_{xx}(1.5,-1.5)=-5.5=f_{yy}(1.5,-1.5)$ and $f_{xy}(1.5,-1.5)=12.5$. From here I conclude that $(1.5,-1.5)$ is a saddle point. However it's supposed to be a point of maximum. What did I do wrong?