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

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

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extreme f(x)=e^{xy}

extreme points

f (x) = e^{x y}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

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

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

ln (x - y) + x^{2} + y

f (x) = x^{101} + x^{51} + x + 1

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