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

The extreme e^{-(x^2+y^2)} is Maximum(0,0)

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extreme e^{-(x^2+y^2)}

extreme points

e^{- (x^{2} + y^{2})}

Maximum (0, 0)

Solution steps

Find the critical points:

(0, 0)

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

D (x, y) = 4 (- 2 e^{- x^{2} - y^{2}} x^{2} + e^{- x^{2} - y^{2}}) (- 2 e^{- x^{2} - y^{2}} y^{2} + e^{- x^{2} - y^{2}}) - 16 e^{2 (- x^{2} - y^{2})} x^{2} y^{2}

Check the sign of at each critical point

Check critical point

(0, 0) :

Maximum

Maximum (0, 0)

f (x) = 478 - x

f (x) = 2 x^{2} ln (x) - 15 x^{2}

(x + 2) e^{\frac{1}{x}}

f (x) = - 3 sin^{2} (x)

f (x) = f (x) = 9 x^{8} + 8 x^{7} - 8 x - 11