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I know title sounds weird but i had to translate it and that was best i could put. Anyhow i have the following function:

$$ f(x) = x\cdot e^{-x^{2}} $$

I have to find the following:
1. Intervals where function is falling and rising ?
2. Convexity intervals
3. Local and global extreems
4. Graph the function

I was sick and was not able to attend the last class so now I'm looking at the following function and questions not knowing where to find the following.

To solve ( 1. ) i assumed i need to find the derivative of the function which I did and I got $ f'(x) = 1 \cdot e^{-x^{2}} + (-2x^2 \cdot e^{-x^{2}}) = e^{-x^{2}} \cdot (-2x^2 + 1) $

Now that i got the 1st derivative of the function i wanted to check following two rules: Function is falling if $ x = f(x) ; x < x + 1 $ and rising $ x = f(x); x + 1 > x $

However I'm compleately lost here.

  • 1
    The function is falling if $f'(x) \lt 0$ and rising if $f'(x) \gt 0$. Since $e^{-x^2} \gt 0$, this changes when $2x^2=1$, i.e. when $x=\pm \sqrt{\frac12}$.2012-12-30
  • 0
    Hints: Here are some [**notes**](http://fym.asu.edu/~tturner/MAT-251/Lesson/Derivatives%2012%20Inflection%20Points.htm) you missed for convexity. Start with a [**plot**](http://www.wolframalpha.com/input/?i=Plot%5Bx+*+Exp%5B-x%5E2%5D%2C%7Bx%2C-5%2C5%7D%5D)2012-12-30
  • 0
    It's driving me nuts, iv been at it for 4h nothing.2012-12-30

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