Find all inflection points

I know to find inflection points you need to compute the 2nd derivative test and set equal to 0. I think I got the 2nd derivative but I'm lost on the rest. Here is the problem with 1st and 2nd derivatives computed:

Problem #1 -

f(x) = e^(-x^2/2) / sqrt[2*pi]

f'(x) = -e^(-x^2/2) / sqrt[2*pi]

f"(x) = e^(-x^2/2) (x^2-1) / sqrt[2*pi]

I have another problem to find inflection pts. No idea where to start:

Problem #2 -

g(x) = e^[(-(x-a)^2)/(2b^2)] / sqrt[2*pi*b^2]

Can anyone help?? These are tough problems!!