- #1
Luscinia
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Homework Statement
Find the critical points for the function g(x, y, z) = x3+xy2+x2+y2+3z2.
Homework Equations
The Attempt at a Solution
I've come up with the following 3 equations (derivatives set so that they are equal to 0)
(1) 3x2+y2+2x=0
(2) 2xy+2y=0
(3) 6z=0
From (3),
z=0
From (2), 2y(x)+2y(1)=0
x+1=0
x=-1
From (1) using what I have obtained from (2), x+1=0
x=-1
3(-1)2+y2+2(-1)=0
3-2+y2=0
1=-y2
y2=-1
I do not know how I am supposed to isolate y in this case since square roots are supposed to be positive. Do I need to get i involved? If so, how?3-2+y2=0
1=-y2
y2=-1