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

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

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

extreme points

f (x, y) = 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)

2 + x - x^{2}

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

f (x, y) = 2 x^{3} + 2 y^{2} - 800 x

f (x) = 3 x^{3} - 4 x^{2} - 6 x + 1

f (x, y) = - 6 x^{2} - y^{2} + 9 x - 5 y + 8

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