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[tex]\f(x,y)= xye^{-1/2(x^2+y^2)}[/tex]

Is there any stationary points for this surface?

Let z = f(x,y)

I found the

[tex]\delta{z}/\delta{x}[/tex] = [tex]y[e^{-1/2(x^2+y^2)} - x^2e^{-1/2(x^2+y^2)}][/tex]

and

[tex]\delta{z}/\delta{x}[/tex] = [tex]x[e^{-1/2(x^2+y^2)} - y^2e^{-1/2(x^2+y^2)}][/tex]

I'm supposed to equate the two equations to get the stationary points (x , y, z) But I couldn't since I could only get [tex]y - x = y^2 - x^2[/tex] from the two equations and that's it.

How do I proceed? Did i do anything wrong?