Consider the picture below:
This is the levels curves for a function $f(x,y)$ where:
- Blue line is the partial derivative of $f(x,y)$ with respect to x
- Red line is the partial derivative of $f(x,y)$ with respect to y
I know that the intersection of the partials are crtical points. However I do not know how to identify other points which might be crtical but not be local max/minimi points. Like the saddle point, what should I look for?