What is the extreme f(x,y)=18y^2+x^2-x^2y ?

The extreme f(x,y)=18y^2+x^2-x^2y is Minimum(0,0),Saddle(6,1),Saddle(-6,1)

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extreme f(x,y)=18y^2+x^2-x^2y

extreme points

f (x, y) = 18 y^{2} + x^{2} - x^{2} y

Minimum (0, 0), Saddle (6, 1), Saddle (- 6, 1)

Solution steps

Find the critical points:

(0, 0), (6, 1), (- 6, 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 36

D (x, y) = 36 (2 - 2 y) - 4 x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(6, 1) :

Saddle

Check critical point

(- 6, 1) :

Saddle

Minimum (0, 0), Saddle (6, 1), Saddle (- 6, 1)

2 (\frac{1}{2})^{x}

f (x) = \frac{( x - 4 ) ^{2}}{x + 10}

f (x) = 4 x - 1

- 2 x^{3} + 3 x^{2} - 12 x

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

What is the extreme f(x,y)=18y^2+x^2-x^2y ?
The extreme f(x,y)=18y^2+x^2-x^2y is Minimum(0,0),Saddle(6,1),Saddle(-6,1)