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I must find and identify (max or min) the local extrema of $f(x) = x^2 e^{-x}$

This is a simple problem if it was in a calculus exam - but it's not. I'm not sure how to structure the solution for an analysis question.

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Do you know how to differentiate $f(x)$ with respect to $x$? –  yohBS May 5 '13 at 10:58
    
Yes, I do. I could solve this if it was a calculus question. –  Goose May 5 '13 at 11:11
    
I don't understand. It is a calculus question. Don't let these names ("analysis", "calculus", "algebra" and so on) mislead you. This is a specific question with a unique solution, regardless of who's the teacher or what class it was given in. –  yohBS May 5 '13 at 11:18
    
About my last comment: see this youtube.com/watch?v=5ZED4gITL28 –  yohBS May 13 '13 at 15:32

1 Answer 1

Hint:

$$\frac{df}{dx}=2x e^{-x}+x^2(-e^{-x})=(2x-x^2)e^{-x}$$

Extrema can occur only when $df/dx=0$, and $e^{-x}$ is always positive.

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