calculus

Find all relative extreme points y=x e^-x

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1. Find the definition of a relative extreme point, for example:
http://en.wikipedia.org/wiki/Extreme_point

hint:
1. find the domain of the function
f(x)=x*e^(-x)
...the domain is (-∞,∞)
2. calculate f'(x), and verify that f'(x) exists within the domain.
3. find the zeroes of f'(x)=0
4. check that the zeroes found in (3) are maxima or minima by evaluating f"(x).
If f"(x)=0, it is an inflection point and is not an extremum, thus not a critical point.

There should be one relative extreme point for the given function on its domain.

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2. I still can't find the answer because I got max (1,1/e)

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3. I had the impression that the question was looking for relative extreme values in calculus, in which case (1,1/e) is the answer. The function tends to -∞ as x-> -∞ and f(x)->0 as x->∞, and is a maximum at x=1 (when y=1/e).

I am sorry that the reference for extreme point in the Wiki article does not refer to the same subject.
Can you check if the following link refers to what you are working on in class?

http://en.wikibooks.org/wiki/Calculus/Extreme_Value_Theorem

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