Find extrema or saddle point when the second derivative test fails
Let $\varepsilon>0$ be arbitrary. $$f(0,\varepsilon)=-\varepsilon^3<0\\ f(0,-\varepsilon)=\varepsilon^3>0$$ implies that $(0,0)$ is a saddle point.
Find extrema or saddle point when the second derivative test fails
Let $\varepsilon>0$ be arbitrary. $$f(0,\varepsilon)=-\varepsilon^3<0\\ f(0,-\varepsilon)=\varepsilon^3>0$$ implies that $(0,0)$ is a saddle point.