What is the extreme f(x,y)=e^{2xy} ?

The extreme f(x,y)=e^{2xy} is Saddle(0,0)

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extreme f(x,y)=e^{2xy}

extreme points

f (x, y) = e^{2 x y}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 4 e^{2 x y} x^{2}

D (x, y) = - 16 e^{4 x y} x y - 4 e^{4 x y}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = ln ∣ x + e^{y} ∣ - sin (5 x y^{2})

f (x) = 3 x e^{x}

x^{4} - 8 x^{2} + 3

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

f (x) = 4 - x^{2}