What is the extreme f(x,y)=338y^2+x^2-x^2y ?

The extreme f(x,y)=338y^2+x^2-x^2y is Minimum(0,0),Saddle(26,1),Saddle(-26,1)

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extreme f(x,y)=338y^2+x^2-x^2y

extreme points

f (x, y) = 338 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (26, 1), Saddle (- 26, 1)

Solution steps

Find the critical points:

(0, 0), (26, 1), (- 26, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 676

D (x, y) = 676 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(26, 1) :

Saddle

Check critical point

(- 26, 1) :

Saddle

Minimum (0, 0), Saddle (26, 1), Saddle (- 26, 1)

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

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

f (x) = x^{2} - 6

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

x^{3} - 6 x^{2}

What is the extreme f(x,y)=338y^2+x^2-x^2y ?
The extreme f(x,y)=338y^2+x^2-x^2y is Minimum(0,0),Saddle(26,1),Saddle(-26,1)