Find and classify the stationary points of :
f(x,y)=(x+y)*e^(-x²-y²)
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 $\displaystyle f_y$:
$\displaystyle f_x=(x+y)e^{-x^2-y^2}(\frac{1}{x+y}-2x)$
$\displaystyle f_y=(x+y)e^{-x^2-y^2}(\frac{1}{x+y}-2y)$
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?