What is the extreme f(x,y)=50y^2+x^2-x^2y ?

The extreme f(x,y)=50y^2+x^2-x^2y is Minimum(0,0),Saddle(10,1),Saddle(-10,1)

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extreme f(x,y)=50y^2+x^2-x^2y

extreme points

f (x, y) = 50 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (10, 1), Saddle (- 10, 1)

Solution steps

Find the critical points:

(0, 0), (10, 1), (- 10, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 100

D (x, y) = 100 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(10, 1) :

Saddle

Check critical point

(- 10, 1) :

Saddle

Minimum (0, 0), Saddle (10, 1), Saddle (- 10, 1)

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

f (x) = 2 - 4 x^{2}

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

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

f (x) = (x - 1) (x + 1) (x + 4)

What is the extreme f(x,y)=50y^2+x^2-x^2y ?
The extreme f(x,y)=50y^2+x^2-x^2y is Minimum(0,0),Saddle(10,1),Saddle(-10,1)