What are the critical points of the function: $f(x,y,z)=\frac{1}{z^2+x^2+1+y^2}$? Identify as a local minima, maxima, or saddle points.
So I know you have to take the gradient and set it equal to $(0,0,0)$. That will get you all your critical points. How do I identify it as a local minima, maxima, or a saddle point?