What is the extreme f(x,y)=x^3-y^2-12x+6y ?

The extreme f(x,y)=x^3-y^2-12x+6y is Maximum(-2,3),Saddle(2,3)

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extreme f(x,y)=x^3-y^2-12x+6y

extreme points

f (x, y) = x^{3} - y^{2} - 12 x + 6 y

Maximum (- 2, 3), Saddle (2, 3)

Solution steps

Find the critical points:

(- 2, 3), (2, 3)

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

D (x, y) = - 12 x

Check the sign of at each critical point

Check critical point

(- 2, 3) :

Maximum

Check critical point

(2, 3) :

Saddle

Maximum (- 2, 3), Saddle (2, 3)

What is the extreme f(x,y)=x^3-y^2-12x+6y ?
The extreme f(x,y)=x^3-y^2-12x+6y is Maximum(-2,3),Saddle(2,3)