Can someone help me find the critical points of function f(x) = |x|e^(1/x) ?

[Mcr99]

Hello, i'm not sure if this is the right place to post a question about functions and my english is really poor at scientific terms.

I'd like to know how to calculate the critical points of the function f(x)= |x|e^(1/x)

 

[stapel]

Hello, i'm not sure if this is the right place to post a question about functions and my english is really poor at scientific terms.

I'd like to know how to calculate the critical points of the function f(x)= |x|e^(1/x)

What is the definition of "critical points"? (here) What does this suggest, as a means of finding critical points? From algebra, you know that the absolute value splits into two linear functions, so this one function can be viewed as being in two parts (that is, as being a piecewise function). What derivative do you get, especially for the absolute value? (here)

When you reply, please include a clear listing of your thoughts and efforts so far, so we can see where things are going sideways. Thank you!

 

[Deleted member 4993]

Hello, i'm not sure if this is the right place to post a question about functions and my english is really poor at scientific terms.

I'd like to know how to calculate the critical points of the function f(x)= |x|e^(1/x)

Goto:

https://www.wolframalpha.com/input/?i=plot+y=+|x|e^(1/x)

and study the plots.

notice that the function has a local minimum.