Find the critical points of $f(x)$ and use the Second Derivative Test (if possible) to determine whether each corresponds to a local minimum or maximum. Let $$f(x) = x\exp\!\left(-x^{2}\right)$$

Critical Point 1 = is what by the Second Derivative Test ? Local Max Local Min Test Fails ?
Critical Point 2 = is what by the Second Derivative Test ? Local Max Local Min Test Fails ?