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.