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) = \frac{4}{9 - x ^{2} - y ^{2}}

x^{2} + 1

\frac{d}{d x} (I n x (1 - x))

f (x) = \frac{2 x ^{3}}{3} - \frac{x ^{2}}{2} - x

y = x^{3} - 6 x^{2} + 9 x - 8