What is the extreme f(x,y)= 23/2 y^4-46xy+23x^2 ?

The extreme f(x,y)= 23/2 y^4-46xy+23x^2 is Saddle(0,0),Minimum(-1,-1),Minimum(1,1)

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extreme f(x,y)= 23/2 y^4-46xy+23x^2

extreme

Saddle (0, 0), Minimum (- 1, - 1), Minimum (1, 1)

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = 138 y^{2}

D (x, y) = 6348 y^{2} - 2116

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Check critical point

(- 1, - 1) :

Minimum

Check critical point

(1, 1) :

Minimum

Saddle (0, 0), Minimum (- 1, - 1), Minimum (1, 1)

What is the extreme f(x,y)= 23/2 y^4-46xy+23x^2 ?
The extreme f(x,y)= 23/2 y^4-46xy+23x^2 is Saddle(0,0),Minimum(-1,-1),Minimum(1,1)