What is the extreme f(x,y)=e^{5xy} ?

The extreme f(x,y)=e^{5xy} is Saddle(0,0)

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extreme f(x,y)=e^{5xy}

extreme points

f (x, y) = e^{5 x y}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 25 e^{5 x y} x^{2}

D (x, y) = - 250 e^{10 x y} x y - 25 e^{10 x y}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = 2 x - y

9 x^{2} ln (x)

f (x) = x^{3} + \frac{3}{2} y^{2} - 3 x y - 124

f (x, y) = 2 x + 2 y

f (s, t) = s^{3} - 2 t^{2} + 8 s t