What is the extreme f(x,y)=x^2y+e^{xy} ?

The extreme f(x,y)=x^2y+e^{xy} is Saddle(0,0)

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extreme f(x,y)=x^2y+e^{xy}

extreme points

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x, y) = 3 x^{2} y - y^{2} + 5 x y^{2}

P (x, y) = 12 x^{6} - 7 x^{3} y - 10 y^{2}

f (x) = x (x - 2)^{2}

f (x, y) = x^{3} - 6 x y + 8 y^{3}

f (x, y) = x^{2} + x^{2} y + y^{2} + 1

What is the extreme f(x,y)=x^2y+e^{xy} ?
The extreme f(x,y)=x^2y+e^{xy} is Saddle(0,0)