What is the extreme f(x,y)=x^3+y^3-192x-300y+2 ?

The extreme f(x,y)=x^3+y^3-192x-300y+2 is Saddle(-8,10),Maximum(-8,-10),Minimum(8,10),Saddle(8,-10)

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extreme f(x,y)=x^3+y^3-192x-300y+2

extreme

Saddle (- 8, 10), Maximum (- 8, - 10), Minimum (8, 10), Saddle (8, - 10)

Solution steps

Find the critical points:

(- 8, 10), (- 8, - 10), (8, 10), (8, - 10)

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

D (x, y) = 36 x y

Check the sign of at each critical point

Check critical point

(- 8, 10) :

Saddle

Check critical point

(- 8, - 10) :

Maximum

Check critical point

(8, 10) :

Minimum

Check critical point

(8, - 10) :

Saddle

Saddle (- 8, 10), Maximum (- 8, - 10), Minimum (8, 10), Saddle (8, - 10)

What is the extreme f(x,y)=x^3+y^3-192x-300y+2 ?
The extreme f(x,y)=x^3+y^3-192x-300y+2 is Saddle(-8,10),Maximum(-8,-10),Minimum(8,10),Saddle(8,-10)