First we find the minimum of the potential.

The second derivative of the potential is

Plugging in

and

shows that

is a local maximum and

is a local minimum. So, we consider small oscillations about

. Define

. We would like to know the force on the particle as a function of

. This can be easily found as follows:

Since we are told to consider only small oscillations about the minimum, we can ignore that

terms. The angular frequency of oscillations in the case where we have a spring with spring constant

is

, so, by analogy, the angular frequency of oscillations here is:

Therefore, answer (D) is correct.