Maximizing and Minimizing Multivariable Equations

[Pengwuino]

Hey guys I am very confused here.. I have no idea how to do this! I need to find the max/mins of this equation and I get lost after finding the partials.

$$f(x,y) = xy(1 - x - y) \\$$
$$f_x (x,y) = y - 2xy - y^2 \\$$
$$f_y (x,y) = x - x^2 - 2xy \\$$

I know I'm suppose to kinda do what you do with single variables... but I am getting lost with these multivariables... any help would be very much appreciated :)

 

[Tide]

To find relative extrema set the gradient of the function to zero. Once you've found candidates, you'll need to determine whether the points are minima, maxima or saddle points.

 

[Pengwuino]

that doesn't seem like how we were being taught in the book. It seemed like they were doing it all algebraicly

 

[benorin]

more simply: set $$f_{x}=f_{y}=0$$ and solve the system for x and y

 

[Tide]

IOW, like benorin said, set the derivatives equal to zero.