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- Homework Statement
- Find the critical points of z(x,y) = xy ( x+y-3)

- Relevant Equations
- At the critical points the partial derivatives wrt x and y are both zero

z

Subtracting one equation from the other gives

y

This leads to the following solutions ( 0 , 0) , (0 ,3) , (3 , 0) but the answer also gives ( 1, 1) as a solution. What have i done wrong to not get this solution ?

Thanks

_{x}= 2xy + y^{2}-3y = 0 and z_{y}= 2xy + x^{2}- 3x = 0Subtracting one equation from the other gives

y

^{2}- 3y = x^{2}- 3x ⇒ y (y-3) = x (x-3)This leads to the following solutions ( 0 , 0) , (0 ,3) , (3 , 0) but the answer also gives ( 1, 1) as a solution. What have i done wrong to not get this solution ?

Thanks