The discussion revolves around finding local maxima, minima, or saddle points for the function f(x,y) = (x-y)(1-xy). Participants are exploring the necessary steps to analyze the function's critical points through partial derivatives.
The discussion has seen participants working through the problem, with some expressing confusion about solving the equations. There is a mention of using elimination to combine equations, and one participant indicates they have figured out a solution, although the specific methods remain unclear.
Participants note difficulties in setting the equations to zero and solving for variables, indicating potential constraints in the problem setup. There is also a correction regarding the partial derivative, which suggests a need for careful verification of calculations.
ahhppull said:Homework Statement
Find the local max/min or saddle points of f(x,y) = (x-y)(1-xy)
Homework Equations
The Attempt at a Solution
I expanded the equation to f(x,y) = x-y-(x^2)y+xy^2.
Then I found the partial derivatives of the function.
fx = 1-2xy +y^2
fy = -x^2-2xy
I'm stuck after this part. Usually I can set the function to 0 and solve for x or y, but I can't do that here.
So, can you solve the problem now?ahhppull said:Oh, I managed to type out the whole fy wrong.
It is -x^2 -1 +2yx
SammyS said:So, can you solve the problem now?
SammyS said:Solve these equations simultaneously:
1-2xy +y2 = 0
-x2 -1 +2yx = 0
Use elimination: add them together.
ahhppull said:Thanks man, figured it out
Ray Vickson said:So what solution or solutions do you get?
RGV
ahhppull said:Oh, I got saddle points at (1,1) and (-1,-1)