I want to determine if a singular point is a local min, max or saddle point.
We are dealing with singular points so we cannot use the hessian matrix.
What I have written, and I think I must of missed something is :
Say we have a function $f(x,y,z)$. To show that $(2,2,2)$ is a saddle point, we want to show :
$\forall \epsilon >0$, we want to find $k,w,h$ such that if $k^2+w^2+h^2<\epsilon^2$ then
And here is where what I have writen is incomplete:
$f(2+k, 2+w, 2+h) > f(2,2,2)$
Is this correct as $f(2-k, 2-w, 2-h)<f(2,2,2)$?
Edit: I'm not sure how standard these terms are, so to be clear a singular point here is a point at which the partial of the function does not exist.