What is the extreme f(x,y)= 1/2 xy ?

The extreme f(x,y)= 1/2 xy is Saddle(0,0)

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extreme f(x,y)= 1/2 xy

extreme points

f (x, y) = \frac{1}{2} x y

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - \frac{1}{4}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = - 2 x^{3} - 5 x^{2} + 4 x y - y^{2} + 4 y - 7

f (x, y) = 5 x^{2} + 5 y^{2} + 5 x y - 10 x - 5 y + 18

f (x) = 3 x^{2} + 3 x + 1

x^{2} + x y + y^{2} - 2 x - y

f (x) = x^{3} + y^{2} + 2 x y - 4 x - 3 y + 5