Find the critical numbers of the function g(y)=y-1/y^2-y+1

So far I've gotten to -y^2+2y+1/(y^2-y+1)^2=0
My teacher said that the answer is suppose to be (0,2) but when I finish out the problem in not getting that what am I doing wrong?

Question

Find the critical numbers of the function g(y)=y-1/y^2-y+1

So far I've gotten to -y^2+2y+1/(y^2-y+1)^2=0
My teacher said that the answer is suppose to be (0,2) but when I finish out the problem in not getting that what am I doing wrong?

alekos · Answer

I take it that your looking for the critical points or stationary points?

anonymous · Answer

Yes

alekos · Answer

g'(y) should be -y^2+2y/(y^2-y+1)

alekos · Answer

so we have g'(y)=0  =>  y^2-2y = 0  solve for y

alekos · Answer

do you follow?

anonymous · Answer

No not really

alekos · Answer

do you understand how i got g'(y)?

anonymous · Answer

Yes I get that part but after trying to solve for y after how you've explained it in still not getting the answer

alekos · Answer

y^2-2y=0
y(y-2)=0
so y=0  and y=2  are the solutions

alekos · Answer

got that now?

anonymous · Answer

Ohhhh ok duh thank you

alekos · Answer

no problem