To analyze the graph of the function, I will interpret the visual features (local maxima, minima, and absolute extrema) based on the given plot.

1. Local Maxima:
   A local maximum occurs at a peak where the function transitions from increasing to decreasing. In this graph, this happens approximately at x ≈ 2 and x ≈ 6.

   Answer: $x = 2, 6$

2. Local Minima:
   A local minimum occurs at a trough where the function transitions from decreasing to increasing. This happens approximately at x ≈ 4.

   Answer: $x = 4$

3. Absolute Maximum:
   The absolute maximum is the highest point on the graph over the interval $[0, 8]$. Observing the graph, the highest point is at x ≈ 0, where the value of the function is approximately 1.

   Answer: $f(0) = 1$

4. Absolute Minimum:
   The absolute minimum is the lowest point on the graph over the interval $[0, 8]$. Observing the graph, the lowest point occurs at x ≈ 5, where the value of the function is approximately $-1$.

   Answer: $f(5) = -1$

Would you like me to explain any of these steps in more detail?

Related Questions:

1. What is the importance of critical points in finding local extrema?
2. How can the derivative test confirm whether points are maxima or minima?
3. Can you describe how to determine if extrema are absolute using endpoints?
4. How do absolute extrema relate to the domain of a function?
5. Why is it essential to include endpoints when finding absolute extrema on a closed interval?

Tip:

When analyzing graphs for extrema, always check transitions in slope direction (increasing to decreasing for maxima, and vice versa for minima) and evaluate endpoints for absolute extrema.