The discussion revolves around the conditions for identifying saddle points in the context of partial derivatives, specifically examining the implications of the second derivative test at a critical point.
Some participants have provided insights regarding the conditions needed for saddle points, while others are seeking clarification on the implications of the critical point status. There appears to be an ongoing exploration of the assumptions involved in the original statement.
There is a mention of the critical point (2,1) and the relationship between the second derivatives, which is central to the discussion. The participants are navigating the definitions and requirements without reaching a definitive conclusion.
lanedance said:wouldn't it need fx(2,1) = fy(2,1) = 0 as well?