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

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

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

extreme points

f (x) = 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)

y e^{x^{2} - y^{2}}

P (x, y) = 3 x^{2} y + 4 x y^{2} - y^{4}

f (x) = 3 x^{5} - 20 x^{3} + 16

\frac{x ^{3}}{x - 2}

f (x) = - x^{2} + 4, - 1 \leq x \leq 2

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