How to find when a function is rising and decreasing I have this assignment that i don't fully understand.
$$f(x) = e^x\sin(x)$$ $$ x \in [0,2\pi]$$
1) decide where the function rises and decreases
2) find all the local maxima and minima and the global maxima and minima
3) decide where the function "curls" up and down
I do not really understand the task, so if someone could explain it will be appreciated.

HINT
As you rightly observe in the comments, it is somewhat poorly worded but should make sense.
Concerning $iii)$ (I think $i), ii)$ are pretty clear), it asks you to find where the function is concave and where it is convex. 
We go about it using the second derivative.
$$f'(x)=e^x\sin x+e^x\cos=e^x(\sin x+\cos x) \Rightarrow\\f''(x)=e^x(\sin x+\cos x)+e^x(\cos x-\sin x)=2e^x\cos x$$
So you need to find the roots of $f''(x)$ in $[0,2\pi]$, that is $\xi\in [0,2\pi]$ such that $f''(\xi)=2e^{\xi}\cos \xi=0$ or equivalently $\cos \xi=0$.
Once you do that you have to make the table of signs to deduce concavity.
