Hi tsr,
What do we do when the second derivative test fails? How do we approach it, and is there a general method to further find whether a critical point is a maximum, minimum or a saddle point?
For example, I'm asked to find all the critical points of the function
f(x,y)=x^2013−y^2013
and determine the nature of the critical points. The critical point that I have found is at (0,0), but I'm unable to determine its nature as the second derivative test fails here.
Any help would be much appreciated