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

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

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

extreme points

f (x, y) = x^{2} y - x^{2} - 2 y^{2}

Maximum (0, 0), Saddle (2, 1), Saddle (- 2, 1)

Solution steps

Find the critical points:

(0, 0), (2, 1), (- 2, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - 4

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Check critical point

(2, 1) :

Saddle

Check critical point

(- 2, 1) :

Saddle

Maximum (0, 0), Saddle (2, 1), Saddle (- 2, 1)

f (x) = 2 x^{3} + 9 x^{2} + 12 x + 1

f (x) = 3 x^{4} - 4 x^{3}

g (x, y) = 9 - x^{2} - y^{2}

f (x) = \frac{x ^{2}}{x ^{2} - 1}

f (x) = 5 - 2 x + 3 x^{2} - x^{3}

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