What is the extreme f(x,y)=y^3-x^3-3xy ?

The extreme f(x,y)=y^3-x^3-3xy is Saddle(0,0),Maximum(1,-1)

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extreme f(x,y)=y^3-x^3-3xy

extreme points

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

Saddle (0, 0), Maximum (1, - 1)

Solution steps

Find the critical points:

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

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

D (x, y) = - 36 x y - 9

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(1, - 1) :

Maximum

Saddle (0, 0), Maximum (1, - 1)

f (x) = 5 x + 10 a

f (x, y) = x^{2} + y^{2} - 20 x + 16 y - 9

4 - 6 x + x^{2}

f (x) = 6 sin (3 x)

f (x) = \frac{e ^{x}}{7 x}

What is the extreme f(x,y)=y^3-x^3-3xy ?
The extreme f(x,y)=y^3-x^3-3xy is Saddle(0,0),Maximum(1,-1)