The graph provided shows a curve with several key points labeled as $a$, $b$, $c$, $d$, $r$, and $s$. I will identify which points correspond to absolute and local extrema, and points that are neither a maximum nor a minimum.

1. Absolute maximum:

• The absolute maximum is the highest point on the entire graph. From the graph, this occurs at point $d$.

2. Absolute minimum:

• The absolute minimum is the lowest point on the entire graph. In this case, point $a$ is the lowest on the graph.

3. Local maximum:

• A local maximum is a peak where the curve changes from increasing to decreasing. In the graph, points $b$ and $d$ are local maxima.

4. Local minimum:

• A local minimum is a trough where the curve changes from decreasing to increasing. From the graph, point $r$ is a local minimum.

5. Neither a maximum nor a minimum:

• Points that do not correspond to any extrema. In this graph, points $c$ and $s$ do not seem to be extrema, so they fall into this category.

Summary of classifications:

• Absolute maximum: $d$
• Absolute minimum: $a$
• Local maximum: $b$, $d$
• Local minimum: $r$
• Neither a maximum nor a minimum: $c$, $s$

Would you like further details on any of these points?

Here are 5 questions for further exploration:

1. What are the conditions for a point to be classified as a local maximum or minimum?
2. How do we determine the absolute maximum and minimum from a given interval?
3. Can a point be both a local and absolute maximum? Why or why not?
4. How can we find critical points from the derivative of a function?
5. What happens to the classification of extrema if the graph extends beyond the visible range?

Tip: When looking for extrema, always check for turning points, where the derivative changes sign. These can help identify local maxima or minima.