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

The extreme f(x,y)=4xy is Saddle(0,0)

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extreme f(x,y)=4xy

extreme points

f (x, y) = 4 x y

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = - 16

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = x^{3} - 9 x^{2} + 24 x

f (x) = - 2 x^{3} + 3 x^{2} + 12 x - 5

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

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

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