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)

x \to 0 lim (\frac{5 ^{x} - 1}{7 x})

\int_{0}^{1} \frac{1}{x ^{2} + 3 x + 2} d x

\int 49 - x^{2} d x

x y^{^{'}} - 4 y = x^{5} e^{x}

\int \frac{1}{4 + 4 x ^{2} + x ^{4}} d x