To analyze this graph and determine the local extrema, let's identify points where the function reaches local minimum or maximum values.

1. Local Minimum:

   • The graph appears to have a local minimum at $x \approx -3$ with $y \approx -5$.
   • Another local minimum appears around $x \approx 6$ with $y \approx 3$.

2. Local Maximum:

   • The graph reaches a local maximum at $x \approx 2$ with $y \approx 8$.

Answers:

• Local minimum at: $x = -3, x = 6$
• Local maximum at: $x = 2$

Would you like further explanation on how to identify these points or any additional details?

Here are five related questions to expand your understanding:

1. How do you differentiate between a local and an absolute extremum on a graph?
2. How can you verify these extrema points by analyzing the function’s derivative?
3. What are inflection points, and how can they be identified on this graph?
4. How would these extrema change if the function’s equation was provided?
5. Why is it important to distinguish between critical points and extrema?

Tip: Local extrema occur at points where the function changes direction, often identified where the derivative equals zero or is undefined.