What is the extreme F(x,z)=x^3+z^3-3x-3z ?

The extreme F(x,z)=x^3+z^3-3x-3z is Saddle(-1,1),Maximum(-1,-1),Minimum(1,1),Saddle(1,-1)

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extreme F(x,z)=x^3+z^3-3x-3z

extreme points

F (x, z) = x^{3} + z^{3} - 3 x - 3 z

Saddle (- 1, 1), Maximum (- 1, - 1), Minimum (1, 1), Saddle (1, - 1)

Solution steps

Find the critical points:

(- 1, 1), (- 1, - 1), (1, 1), (1, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = 6 z

D (x, z) = 36 x z

Check the sign of at each critical point

Check critical point

(- 1, 1) :

Saddle

Check critical point

(- 1, - 1) :

Maximum

Check critical point

(1, 1) :

Minimum

Check critical point

(1, - 1) :

Saddle

Saddle (- 1, 1), Maximum (- 1, - 1), Minimum (1, 1), Saddle (1, - 1)

f (x) = \frac{x ^{4} + 1}{x ^{2}}

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

x^{2} + y^{2}

f (x, y) = 4 x^{2} + 9 y^{2}

f (x) = 6 x^{5} - 40 x^{3} + 14

What is the extreme F(x,z)=x^3+z^3-3x-3z ?
The extreme F(x,z)=x^3+z^3-3x-3z is Saddle(-1,1),Maximum(-1,-1),Minimum(1,1),Saddle(1,-1)