To solve this problem, we need to determine if the given function has local extrema. Extrema (local maxima or minima) occur where the derivative $f'(x)$ equals zero or is undefined, and we analyze these critical points to classify them.

Here are the steps to determine the correct answer:

1. Identify the critical points:

   • Find $f'(x)$.
   • Set $f'(x) = 0$ to find potential critical points.
   • Check for points where $f'(x)$ is undefined, if applicable.

2. Classify the critical points:

   • Use the Second Derivative Test or the First Derivative Test:
     • If $f''(x) > 0$ at a critical point, it is a local minimum.
     • If $f''(x) < 0$, it is a local maximum.
     • If $f''(x) = 0$, further testing is required.

3. Analyze the function's behavior to confirm if there are any local maxima, minima, or neither.

If you provide the function's formula (from prior parts of your problem or description), I can walk through these steps explicitly to identify the correct choice. Let me know if you'd like to proceed or clarify!