What is the extreme f(x,y)=242y^2+x^2-x^2y ?

The extreme f(x,y)=242y^2+x^2-x^2y is Minimum(0,0),Saddle(22,1),Saddle(-22,1)

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extreme f(x,y)=242y^2+x^2-x^2y

extreme points

f (x, y) = 242 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (22, 1), Saddle (- 22, 1)

Solution steps

Find the critical points:

(0, 0), (22, 1), (- 22, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 484

D (x, y) = 484 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(22, 1) :

Saddle

Check critical point

(- 22, 1) :

Saddle

Minimum (0, 0), Saddle (22, 1), Saddle (- 22, 1)

- 4 x + 9 x^{\frac{4}{9}}

f (x) = e^{- (x - 1)^{2}}

f (x, y) = \frac{1}{3} x^{3} + y^{3} + 2 x^{2} - 12 x - 3 y

f (x) = 6 + 3 x^{2} - 2 x^{3}

f (x) e^{2 x} (x^{2} - 3 x + 2)

What is the extreme f(x,y)=242y^2+x^2-x^2y ?
The extreme f(x,y)=242y^2+x^2-x^2y is Minimum(0,0),Saddle(22,1),Saddle(-22,1)