Hugh,
you can select the domain by specifying it as the third argument to NSolve:
NSolve[f[x]/f'[x] == 0, x, Reals]
will give you the two real solutions:
{{x -> -0.76146}, {x -> 0.}}
As you can see, what you get out of NSolve is a list of replacements (well, actually a list of a list of replacements, since NSolve can handle multivariate functions). To pass the values to other functions, you could extract the value(s) for example by applying the replacement list(s) to your variable(s):
x /. NSolve[f[x]/f'[x] == 0, x, Reals]
Will give you a list with your solution(s):
{-0.76146, 0.}
You could for example apply every element of the list to a function:
g/@(x /. NSolve[f[x]/f'[x] == 0, x, Reals]) (*equivalent with*)
g[#] & /@ (x /. NSolve[f[x]/f'[x] == 0, x, Reals])
Or if you want to extract one of the solutions manually:
(x /. NSolve[f[x]/f'[x] == 0, x, Reals])[[1]]
Hope that helps!
Patrik