What is the extreme F(x,y)=x^3-6xy+3y^2+1 ?

The extreme F(x,y)=x^3-6xy+3y^2+1 is Minimum(2,2),Saddle(0,0)

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extreme F(x,y)=x^3-6xy+3y^2+1

extreme points

F (x, y) = x^{3} - 6 x y + 3 y^{2} + 1

Minimum (2, 2), Saddle (0, 0)

Solution steps

Find the critical points:

(2, 2), (0, 0)

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

D (x, y) = 36 x - 36

Check the sign of at each critical point

Check critical point

(2, 2) :

Minimum

Check critical point

(0, 0) :

Saddle

Minimum (2, 2), Saddle (0, 0)

What is the extreme F(x,y)=x^3-6xy+3y^2+1 ?
The extreme F(x,y)=x^3-6xy+3y^2+1 is Minimum(2,2),Saddle(0,0)