The question asks to find intervals where the function $y = f(x)$, based on the given graph, is increasing, decreasing, and also to identify the local maximum and minimum points.

Step-by-step analysis:

1. Increasing intervals: The function is increasing where the slope of the graph is positive, i.e., the curve is moving upwards as you move from left to right.

2. Decreasing intervals: The function is decreasing where the slope is negative, i.e., the curve is moving downwards as you move from left to right.

3. Local maximum: This occurs at the peak of a curve, where the function switches from increasing to decreasing.

4. Local minimum: This occurs at the bottom of a curve, where the function switches from decreasing to increasing.

Visual analysis of the graph:

• The function increases on the interval from approximately $x = -1$ to $x = 1.5$.
• The function decreases on the interval from approximately $x = 1.5$ to $x = 4$.
• After $x = 4$, the function begins increasing again.

Local extrema:

• Local maximum: Near $x = 1.5$, where the graph reaches its highest point before starting to decrease.
• Local minimum: Near $x = 4$, where the graph reaches its lowest point before starting to increase again.

Would you like further details on how to determine these intervals or any other clarification?

Here are 5 relative questions for further exploration:

1. How can you use derivatives to confirm increasing or decreasing behavior of a function?
2. What is the formal definition of a local maximum and local minimum?
3. How can concavity be analyzed using the second derivative?
4. What are the global extrema, and how do they differ from local extrema?
5. How can inflection points be determined from a function's graph?

Tip: To analyze the behavior of a function in terms of increasing and decreasing, you can always use the first derivative test. The function is increasing where the derivative is positive and decreasing where the derivative is negative.