# Thread: Question on stationary points

1. ## Question on stationary points

Find and classify the stationary points of :
f(x,y)=(x+y)*e^(-x²-y²)

2. I think it means find the critical points.

3. Thing is that i can do stationary points with 1 variable involved but this one has two,not used to it.
help plsss

4. Um then I'm assuming you don't know partial derivatives. Just in case you do, you should do the following:

Find $\displaystyle f_x$ and $\displaystyle f_y$, set them equal to 0, and solve for x and y.

I got this for $\displaystyle f_x$ and $\displaystyle f_y$:

$\displaystyle f_x=(x+y)e^{-x^2-y^2}(\frac{1}{x+y}-2x)$

$\displaystyle f_y=(x+y)e^{-x^2-y^2}(\frac{1}{x+y}-2y)$

5. Originally Posted by goaway716
Thing is that i can do stationary points with 1 variable involved but this one has two,not used to it.
help plsss
Haven't you been taught this material? If not, then why are you attempting this question. If you have been taught it, then your class notes or textbook should provide enough help to at least get you started - what have you tried and where are you stuck?

6. yes i have done whatever i could have but i just want to make sure whether i am on the right track and need some guidance.
This is what i have tried :

Take the partial derivatives d/dx and d/dy. So:

(d/dx) f(x,y)=(d/dx)[(x+y)*e^(-x²-y²)] =e^(-x²-y²) +(e^(-x²-y²))(-2x)= e^(-x²-y²)[1-2x]=0 iff x=1/2.

The y-case is symmetrical, so (d/dy) f(x,y)=0 iff y=1/2.

They are then both equal to zero at the point

(1/2,1/2, z). Substituting , this is (1/2,1/2,e^(-1/2))

this is it..any mistake?