What is the extreme f(x,y)=-y^2+y^2x-x^2+x ?

The extreme f(x,y)=-y^2+y^2x-x^2+x is Maximum(1/2 ,0),Saddle(1,1),Saddle(1,-1)

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extreme f(x,y)=-y^2+y^2x-x^2+x

extreme

Maximum (\frac{1}{2}, 0), Saddle (1, 1), Saddle (1, - 1)

Solution steps

Find the critical points:

(\frac{1}{2}, 0), (1, 1), (1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 2 x - 2

D (x, y) = - 2 (2 x - 2) - 4 y^{2}

Check the sign of at each critical point

Check critical point

(\frac{1}{2}, 0) :

Maximum

Check critical point

(1, 1) :

Saddle

Check critical point

(1, - 1) :

Saddle

Maximum (\frac{1}{2}, 0), Saddle (1, 1), Saddle (1, - 1)

What is the extreme f(x,y)=-y^2+y^2x-x^2+x ?
The extreme f(x,y)=-y^2+y^2x-x^2+x is Maximum(1/2 ,0),Saddle(1,1),Saddle(1,-1)