What is the extreme f(x,y)=(x-y)(36-xy) ?

The extreme f(x,y)=(x-y)(36-xy) is Saddle(6,6),Saddle(-6,-6)

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extreme f(x,y)=(x-y)(36-xy)

extreme points

f (x, y) = (x - y) (36 - x y)

Saddle (6, 6), Saddle (- 6, - 6)

Solution steps

Find the critical points:

(6, 6), (- 6, - 6)

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

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

Check the sign of at each critical point

Check critical point

(6, 6) :

Saddle

Check critical point

(- 6, - 6) :

Saddle

Saddle (6, 6), Saddle (- 6, - 6)

f (x) = x^{\frac{8}{3}}

f (x) = x^{2} - 9 y x^{2} - 7 x + 12

f (x) = 2 x^{3} - 9 x^{2} + 12 x + 6

f (x) = x + ln (1 - x)

f (x) = 7 x ln (x)

What is the extreme f(x,y)=(x-y)(36-xy) ?
The extreme f(x,y)=(x-y)(36-xy) is Saddle(6,6),Saddle(-6,-6)