What is the extreme e^{(y^2)/4-x^2-1} ?

The extreme e^{(y^2)/4-x^2-1} is Saddle(0,0)

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extreme e^{(y^2)/4-x^2-1}

extreme points

e^{\frac{y ^{2}}{4} - x^{2} - 1}

Saddle (0, 0)

Solution steps

Find the critical points:

(0, 0)

\frac{\partial ^{2} f}{\partial y ^{2}} = - 2 (- 2 e^{\frac{y ^{2}}{4} - x^{2} - 1} x^{2} + e^{\frac{y ^{2}}{4} - x^{2} - 1})

D (y, x) = e^{\frac{- 4 x ^{2} + y ^{2} - 2}{2} - 1} y^{2} x^{2} - \frac{e ^{\frac{y ^{2} - 4 x ^{2} - 4}{2}} y ^{2}}{2} + 2 e^{\frac{- 4 x ^{2} + y ^{2} - 2}{2} - 1} x^{2} - e^{\frac{y ^{2} - 4 x ^{2} - 2}{2} - 1} - e^{\frac{y ^{2} - 4 x ^{2} - 4}{2}} y^{2} x^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Saddle

Saddle (0, 0)

f (x) = 6 x^{2} - 4 x + 1, 0 < x < 8

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

f (x) = \frac{69120}{x} + \frac{69120}{y} + 5 x y

f (x) = x^{\frac{2}{3}} (x + 1)

f (x) = x^{2} + 4 x (\frac{4000}{x ^{2}})

What is the extreme e^{(y^2)/4-x^2-1} ?
The extreme e^{(y^2)/4-x^2-1} is Saddle(0,0)