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 points

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

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)

f (x) = 5 + 9 x^{2} - 6 x^{3}

f (x, y) = 6 - x^{2} - 4 y^{2}

f (x) = 2 x^{2} + \frac{2048}{x} + 13

f (x) = (x + 3)^{\frac{4}{3}}, - 6 \leq x \leq 6

x y - 2 x - 2 y - x^{2} - y^{2}

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)