What is the critical f(x,y)=xe^{-2x^2-2y^2} ?

The critical f(x,y)=xe^{-2x^2-2y^2} is (-1/2 ,0),(1/2 ,0),(-1/2 ,0),(1/2 ,0)

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critical f(x,y)=xe^{-2x^2-2y^2}

critical points

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

(- \frac{1}{2}, 0), (\frac{1}{2}, 0), (- \frac{1}{2}, 0), (\frac{1}{2}, 0)

Solution steps

x e^{- 2 x^{2} - 2 y^{2}}

Find where

\nabla f (x, y)

is equal to zero or undefined

(- \frac{1}{2}, 0), (\frac{1}{2}, 0), (- \frac{1}{2}, 0), (\frac{1}{2}, 0)

f (x) = x^{4} + x^{2} (y - 2) + 9 (y - 1)^{2}

f (x) = x^{4} - 2 x^{2} + y^{2} - 4 y

f (x) = 4 x^{3} - 6 x^{2}

f (x) = x^{3} - 9 x^{2} + 24 x - 7

f (x) = x^{2} - 2 x y + 2 y^{2} + 4 x - 8 y + 24

What is the critical f(x,y)=xe^{-2x^2-2y^2} ?
The critical f(x,y)=xe^{-2x^2-2y^2} is (-1/2 ,0),(1/2 ,0),(-1/2 ,0),(1/2 ,0)