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

The extreme g(x,y)=x^3-2y^2-2y^4+3x^2y is Saddle(-1, 1/2),Maximum(-2,1)

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

extreme

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

Solution steps

Find the critical points:

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

\frac{\partial ^{2} f}{\partial x ^{2}} = - 24 y^{2} - 4

D (x, y) = (6 x + 6 y) (- 24 y^{2} - 4) - 36 x^{2}

Check the sign of at each critical point

Check critical point

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

Saddle

Check critical point

(- 2, 1) :

Maximum

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

What is the extreme g(x,y)=x^3-2y^2-2y^4+3x^2y ?
The extreme g(x,y)=x^3-2y^2-2y^4+3x^2y is Saddle(-1, 1/2),Maximum(-2,1)