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

The extreme f(x,y)=-e^{x-y^2+xy} is Saddle(-2,-1)

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

extreme

Saddle (- 2, - 1)

Solution steps

Find the critical points:

(- 2, - 1)

\frac{\partial ^{2} f}{\partial x ^{2}} = - e^{x - y^{2} + x y} (- 2 y + x)^{2} + 2 e^{x - y^{2} + x y}

D (x, y) = - e^{x - y^{2} + x y} (y + 1)^{2} (- e^{x - y^{2} + x y} (- 2 y + x)^{2} + 2 e^{x - y^{2} + x y}) - (2 e^{x - y^{2} + x y} y^{2} + 2 e^{x - y^{2} + x y} y - e^{x - y^{2} + x y} x y - e^{x - y^{2} + x y} x - e^{x - y^{2} + x y})^{2}

Check the sign of at each critical point

Check critical point

(- 2, - 1) :

Saddle

Saddle (- 2, - 1)

What is the extreme f(x,y)=-e^{x-y^2+xy} ?
The extreme f(x,y)=-e^{x-y^2+xy} is Saddle(-2,-1)