What is the extreme f(x)=200y^2+x^2-x^2y ?

The extreme f(x)=200y^2+x^2-x^2y is Minimum(0,0),Saddle(20,1),Saddle(-20,1)

extreme f(x)=200y^2+x^2-x^2y

extreme points

f (x) = 200 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (20, 1), Saddle (- 20, 1)

Solution steps

Find the critical points:

(0, 0), (20, 1), (- 20, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 400

D (x, y) = 400 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(20, 1) :

Saddle

Check critical point

(- 20, 1) :

Saddle

Minimum (0, 0), Saddle (20, 1), Saddle (- 20, 1)

f (x) = x^{4} - 4 x^{3} - x^{2} + 12 x - 2

f (x) = x^{2} + x y + y^{2} - 28 y + 261

\frac{- x + 3}{x ^{2} + 14 x + 49}

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

f (x) = - 2 cos (2 x)

What is the extreme f(x)=200y^2+x^2-x^2y ?
The extreme f(x)=200y^2+x^2-x^2y is Minimum(0,0),Saddle(20,1),Saddle(-20,1)