Finding points which are not local maximum or minimum

Question

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?

Answer 1

You should check the second order derivative.

Second derivative test