Question

how to solve for critical parts given f_x= 2x+2xy =0 and f_y=2y+x^2=0?

Answer 1

for some reason I always have problems with solving the equation I used substitution and I got x(2+x^2)=0 as the final bit

Answer 2

given
f_x= 2x+2xy =0 ..............1)... and
f_y=2y+x^2=0..................2)
on eq 2) if x=0 , 2y+x^2=0..is y=0 ? yes?
how about x=+ - sqrt (2) , 2y= -(+,- sqrt2)^2
y=-2/2=-1 ? yes or no?
is the critical point (0,0)? and (+sqrt2,-1)?,(-sqrt2,-1)? yes or no?