determine the intervals where f(x) = e^((-x^2)/2) is increasing and where it is decreasing
1. Find f'(x)=-xe^((-x^2)/2)
2. plot f'(x) and find where f'(x) crosses the x-axis.
Note that e^((-x^2)/2)>0 ∀ x∈R. Therefore the sign is determined by the factor (-x), which is >0 for x∈(-∞0) and negative for x∈ (0,+∞).
3. Knowing that x is increasing when f'(x)>0 and decreasing when f'(x)<0, can you take it from here?