Let $f(x) = 2\sqrt{x}e^{-x}.$ Answer the following questions.

---

1. Find the interval(s) on which $f$ is increasing.
Answer (in interval notation):

2. Find the interval(s) on which $f$ is decreasing.
Answer (in interval notation):

3. Find the local maxima of $f.$ List your answers as points in the form $(a,b)$.
Answer (separate by commas):

4. Find the local minima of $f.$ List your answers as points in the form $(a,b)$.
Answer (separate by commas):

5. Find the interval(s) on which $f$ is concave upward.
Answer (in interval notation):

6. Find the interval(s) on which $f$ is concave downward.
Answer (in interval notation):

---