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

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

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

extreme points

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

Minimum (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 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, 1) :

Saddle

Check critical point

(- 2, 1) :

Saddle

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

f (x) = \frac{x}{x ^{2} + 100}

f (x) = \frac{4}{3} x^{3} + 4 x^{2} - 252 x + 7

f (x) = 4 x - 9 x^{\frac{4}{9}}

f (x, y) = 3 x^{3} - 9 x + 9 x y^{2}

f (x) = 2 x^{2} - 8 x + y^{2} - 8 y + 2

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