Local Minimum of y=x(e^1/x): Why Not (1,e)?

[nickeisenberg]

I found that the local minimum of y=x(e^1/x) is (1,e) but can someone tell me why the absolute minimum is also not (1,e) and can someone tell me why this function does not have an absolute minimum? Thanks

 

[chiro]

I found that the local minimum of y=x(e^1/x) is (1,e) but can someone tell me why the absolute minimum is also not (1,e) and can someone tell me why this function does not have an absolute minimum? Thanks

Hey nickeisenberg and welcome to the forums.

Just to clarify, what is the domain of your function?

 

[nickeisenberg]

all reals number except 0

 

[Ultramilk]

y= x (e^1/x)

Think about the two components.
If x -> -∞
x -> -∞
e^(1/x) -> 1 (1/-∞) ~ 0, e^0 = 1