What is the extreme f(x,y)=e^{3xy} ?

The extreme f(x,y)=e^{3xy} is Saddle(0,0)

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extreme f(x,y)=e^{3xy}

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial x ^{2}} = 9 e^{3 x y} x^{2}

D (x, y) = - 54 e^{6 x y} x y - 9 e^{6 x y}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

P (x, y) = 3 x + 2 y

3 y^{2} - 2 y^{3} - 3 x^{2} + 6 x y

\frac{5 x}{x ^{2} - 16}

f (x, y) = 3 x^{3} - 9 x y + 3 y^{3}

f (x) = 6 - 2 x