What is the extreme f(x,y)=xy-2x-4y ?

The extreme f(x,y)=xy-2x-4y is Saddle(4,2)

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extreme f(x,y)=xy-2x-4y

extreme points

f (x, y) = x y - 2 x - 4 y

Saddle (4, 2)

Solution steps

Find the critical points:

(4, 2)

\frac{\partial ^{2} f}{\partial x ^{2}} = 0

D (x, y) = - 1

Check the sign of at each critical point

Check critical point

(4, 2) :

Saddle

Saddle (4, 2)

f (x) = 4 x^{2} - 5 x + 1

f (x) = x^{3} - 4 x^{2} - 3 x + 6

f (x) = x^{3} - 4 x^{2} - 3 x + 8

x^{3} - 6

2 x^{3} - 6 x^{2} + 6 x + 1

What is the extreme f(x,y)=xy-2x-4y ?
The extreme f(x,y)=xy-2x-4y is Saddle(4,2)