# Thread: local maxima and minima

1. ## local maxima and minima

How would you find the local maxima and minima for y= xe^-x

Im not sure how to do it and would appreciate very much if someone could help me.

2. Generally, you would examine it for continuity, then find the first derivative. Where the first derivative exists and is zero, this is likely to be a local max or min. That's only part of the story, of course. You tell me the rest.

Can you find dy/dx? It will take the Product Rule.

3. so y'= (e^-x)(-x e^-x)
= e^-x(1-x)

so do u let y'= 0?

if so, i put e^-x(1-x)=0 and thats when i got stuck

so what do i do next?

4. Originally Posted by fvaras89
so y'= (e^-x)(-x e^-x)
= e^-x(1-x)

so do u let y'= 0?

if so, i put e^-x(1-x)=0 and thats when i got stuck

so what do i do next?
Well, obviously either $\displaystyle e^{-x} = 0$ or $\displaystyle (1 - x) = 0$ .... (Hint: $\displaystyle e^{-x} = 0$ has no real solution ....)

5. Personally, I'm a little curious how how got from here

Originally Posted by fvaras89
so y'= (e^-x)(-x e^-x)
to here

= e^-x(1-x)
Seems to be some notational difficulty requiring magic to get to the right result. Please be more careful. You WILL unconfuse yourself.

6. I just thought u could take out the common factor like i did before or would there be another way to present it?

7. I think it would help if the addition actually appeared in the first equation. Thus my encouragement to be more careful. I have little doubt that you had the correct thing in your mind, you just didn't write it.