The form of the derivative is not certain: some of you used a straight line as the derivative. Without more information, it's hard to say who is right! One would have to very carefully measure the slopes to do better. This graph could certainly be correct. It satisfies the crucial requirements that it's negative to the left of the point x=0, 0 at 0, and positive to the right.
Note that this student includes the domains for both g and g', and that the domain for g' is slightly smaller than that of g (because the denominator must not be 0).