I think it means find the critical points.
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?