What is the extreme F(x,y)=x^2y^3-xy-y ?

The extreme F(x,y)=x^2y^3-xy-y is Saddle(2, 1/2),Saddle(2,-1/2)

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extreme F(x,y)=x^2y^3-xy-y

extreme

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 x^{2} y

D (x, y) = - 24 x^{2} y^{4} + 12 x y^{2} - 1

Check the sign of at each critical point

Check critical point

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

Saddle

Check critical point

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

Saddle

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

What is the extreme F(x,y)=x^2y^3-xy-y ?
The extreme F(x,y)=x^2y^3-xy-y is Saddle(2, 1/2),Saddle(2,-1/2)