What is the extreme f(x,y)=-x^4-32x+y^3-12y+7 ?

The extreme f(x,y)=-x^4-32x+y^3-12y+7 is Saddle(-2,2),Maximum(-2,-2)

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extreme f(x,y)=-x^4-32x+y^3-12y+7

extreme points

f (x, y) = - x^{4} - 32 x + y^{3} - 12 y + 7

Saddle (- 2, 2), Maximum (- 2, - 2)

Solution steps

Find the critical points:

(- 2, 2), (- 2, - 2)

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

D (x, y) = - 72 x^{2} y

Check the sign of at each critical point

Check critical point

(- 2, 2) :

Saddle

Check critical point

(- 2, - 2) :

Maximum

Saddle (- 2, 2), Maximum (- 2, - 2)

What is the extreme f(x,y)=-x^4-32x+y^3-12y+7 ?
The extreme f(x,y)=-x^4-32x+y^3-12y+7 is Saddle(-2,2),Maximum(-2,-2)