To address this question, we'll need to analyze the function $f$, which is not explicitly provided in your request. Normally, we would investigate the critical points and behavior of the function to identify its extreme points. Here’s a typical approach to determining which of the options applies:

1. Find the critical points: These are where the derivative $f'(x)$ is zero or undefined. Critical points are potential locations for maxima, minima, or saddle points.

2. Examine endpoints (if applicable): For a function defined over a closed interval, we also need to evaluate the function at the endpoints to determine absolute extrema.

3. Determine behavior at critical points and endpoints: The second derivative test $f''(x)$ or first derivative test can help classify each critical point as a maximum, minimum, or neither.

4. Assess the behavior as $x \to \infty$ or $x \to -\infty$: For functions defined on open intervals, we examine limits to infer whether the function has absolute extrema at infinity or if it lacks them.

Now, considering the choices:

• Choice A describes a situation where the function has an absolute maximum at a particular point, but no absolute minimum.
• Choice B describes a function with an absolute minimum, but no absolute maximum.
• Choice C describes a function that has both an absolute minimum and maximum at specific points.
• Choice D indicates no local extreme points at all.

To proceed with solving this, I would need either the function itself or information on its derivative or graphical behavior. Could you provide that, or clarify further? That will help in selecting the correct option.

Possible Follow-up Questions:

1. What is the function $f(x)$ you're working with?
2. Have you calculated the first and second derivatives of the function?
3. Is the function defined over a closed interval or over $(-\infty, \infty)$?
4. Do you know if the function has any critical points?
5. Are there any given limits as $x \to \infty$ or $x \to -\infty$?

Tip:

When determining extrema, always check the endpoints of the domain (if applicable) along with critical points inside the domain.