- #1
dyn
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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
zx = 2xy + y2 -3y = 0 and zy = 2xy + x2 - 3x = 0
Subtracting one equation from the other gives
y2 - 3y = x2- 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
Subtracting one equation from the other gives
y2 - 3y = x2- 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