What is the extreme x^2y+y^2-4y ?

The extreme x^2y+y^2-4y is Minimum(0,2),Saddle(2,0),Saddle(-2,0)

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extreme x^2y+y^2-4y

extreme

Minimum (0, 2), Saddle (2, 0), Saddle (- 2, 0)

Solution steps

Find the critical points:

(0, 2), (2, 0), (- 2, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 2) :

Minimum

Check critical point

(2, 0) :

Saddle

Check critical point

(- 2, 0) :

Saddle

Minimum (0, 2), Saddle (2, 0), Saddle (- 2, 0)

What is the extreme x^2y+y^2-4y ?
The extreme x^2y+y^2-4y is Minimum(0,2),Saddle(2,0),Saddle(-2,0)