The discussion revolves around finding and classifying relative extrema and saddle points of the multivariable function f(x, y) = xy - x^3 - y^2. Participants are exploring the conditions under which these points can be identified and classified.
Some participants suggest that a saddle point can be identified when D < 0, regardless of the value of fxx. Others express confusion about the relationship between these conditions and seek clarification on the classification process.
There is a mention of needing to find locations where both first partial derivatives are zero, indicating a requirement for critical points in the analysis. The discussion also references a specific course, suggesting a shared educational context among participants.
You need to find locations where both of the 1st partial derivatives are zero.Doug_West said:Homework Statement
Find and classify all relative extrema and saddle points of the function
f(x; y) = xy - x^3 - y^2.
Homework Equations
D = fxx *fyy -fxy^2
The Attempt at a Solution
I got D < 0 where D = -1 and fxx = 0, when x=0 and y=0. However I am unsure as to the conclusion I should arrive at when D < 0 but fxx = 0. I'm thinking that this is a saddle point?
Thanks for the help in advance,
Dough