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

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

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

extreme

Minimum (0, 0), Saddle (2, 0)

Solution steps

Find the critical points:

(0, 0), (2, 0)

\frac{\partial ^{2} f}{\partial y ^{2}} = 2 e^{- y}

D (y, x) = 2 e^{- 2 y} y^{2} - 8 e^{- 2 y} y - 2 e^{- 2 y} x^{2} + 4 e^{- 2 y}

Check the sign of at each critical point

Check critical point

(0, 0) :

Minimum

Check critical point

(2, 0) :

Saddle

Minimum (0, 0), Saddle (2, 0)

What is the extreme e^{-y}(x^2+y^2) ?
The extreme e^{-y}(x^2+y^2) is Minimum(0,0),Saddle(2,0)