What is the extreme f(x,y)=x^3-3x+y^2-y^4 ?

The extreme f(x,y)=x^3-3x+y^2-y^4 is

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extreme f(x,y)=x^3-3x+y^2-y^4

extreme points

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

Saddle (- 1, 0), Maximum (- 1, - \frac{1}{2}), Maximum (- 1, \frac{1}{2}), Minimum (1, 0), Saddle (1, - \frac{1}{2}), Saddle (1, \frac{1}{2})

Solution steps

Find the critical points:

(- 1, 0), (- 1, - \frac{1}{2}), (- 1, \frac{1}{2}), (1, 0), (1, - \frac{1}{2}), (1, \frac{1}{2})

\frac{\partial ^{2} f}{\partial x ^{2}} = - 12 y^{2} + 2

D (x, y) = 6 x (- 12 y^{2} + 2)

Check the sign of at each critical point

Check critical point

(- 1, 0) :

Saddle

Check critical point

(- 1, - \frac{1}{2}) :

Maximum

Check critical point

(- 1, \frac{1}{2}) :

Maximum

Check critical point

(1, 0) :

Minimum

Check critical point

(1, - \frac{1}{2}) :

Saddle

Check critical point

(1, \frac{1}{2}) :

Saddle

Saddle (- 1, 0), Maximum (- 1, - \frac{1}{2}), Maximum (- 1, \frac{1}{2}), Minimum (1, 0), Saddle (1, - \frac{1}{2}), Saddle (1, \frac{1}{2})

f (x) = (x - 10)^{\frac{1}{3}}

y = (2 x - 1)^{2}

f (x) = 3 x + \frac{147}{x}

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

2 cos (x) + 2 sin (x)

What is the extreme f(x,y)=x^3-3x+y^2-y^4 ?
The extreme f(x,y)=x^3-3x+y^2-y^4 is