Finding local max/min of a multivariable function. I get stuck in the algebra part.

Question

chupacabraj · Answer

$$F(x,y)= (x-y)(1-xy)$$
FOIL
$$f(x,y) = x-x^2y-y+xy^2$$

chupacabraj · Answer

$$f_{xx}= 1-2xy+y^2$$
$$f_{yy}= -x^2-1+x$$

chupacabraj · Answer

So I get stuck when trying to find the critical points. I attempted by solving by elimination but it turned out ugly.

zepdrix · Answer

If this is f,$$\rm f(x,y) = x-x^2y-y+xy^2$$then don't you mean to call this f_x? The first derivative?$$\rm f_{x}= 1-2xy+y^2$$

zepdrix · Answer

$$\rm f_{xx}=-2y$$

owen3 · Answer

Did you solve $ \nabla f (x,y) = \vec 0 $

owen3 · Answer

$$ -2xy+y^2+1 = 0
\ -x^2+2xy-1 = 0
\ \, \  
\ 
x=1, ~ y = 1
\ x = -1 , ~ y = -1
$$

chupacabraj · Answer

Oh that's right, I meant first derivatives.

chupacabraj · Answer

How did you solve for x and y?

irishboy123 · Answer

|dw:1480583523018:dw|