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

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

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

extreme points

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

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

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

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 12 x^{3} + 2 x^{2} - 3

f (x) = - \frac{21}{2} x^{2} + 24.63 x - 0.21

f (x) = - 0.020148 x^{2} + 0.3862 x - 1.065

f (x) = x^{3} - 2 x^{2} - 4 x + 3, - 1 \leq x \leq 3

f (x) = - 12 x^{5} + 45 x^{4} + 40 x^{3} - 3

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