Let's analyze the graph of the function step by step and solve the questions.

Part (a) Local Maxima and Minima:

We need to identify the local maxima and minima by estimating the coordinates of the points where the graph reaches a peak (max) or a trough (min).

1. First Local Maximum (smaller x-value):
   Looking at the graph, the first local maximum occurs near $x = -5$, and the corresponding $y$-value is approximately 10.
   So, the first local maximum is $(x, y) = (-5, 10)$.

2. Second Local Maximum (larger x-value):
   The second local maximum occurs near $x = 5$, and the $y$-value is approximately 5.
   So, the second local maximum is $(x, y) = (5, 5)$.

3. Local Minimum:
   The local minimum occurs near $x = 0$, and the corresponding $y$-value is approximately $-10$.
   So, the local minimum is $(x, y) = (0, -10)$.

Part (b) Intervals of Increasing and Decreasing:

• Increasing intervals:
  The function is increasing where the slope of the graph is positive. This occurs between:

  1. $(-\infty, -5)$
  2. $(0, 5)$

• Decreasing intervals:
  The function is decreasing where the slope of the graph is negative. This occurs between:

  1. $(-5, 0)$
  2. $(5, \infty)$

Final Answers:

(a) Local extrema:

• First local maximum: $(-5, 10)$
• Second local maximum: $(5, 5)$
• Local minimum: $(0, -10)$

(b) Intervals of increasing and decreasing:

• Increasing: $(-\infty, -5) \cup (0, 5)$
• Decreasing: $(-5, 0) \cup (5, \infty)$

Do you have any questions or need further clarification on any part of the solution?

Here are 5 related questions to expand your understanding:

1. How would you find the global maximum of the function from the graph?
2. What is the importance of identifying local maxima and minima in real-world scenarios?
3. How does calculus help in determining the exact points of local maxima and minima?
4. Can a function have multiple local maxima but no global maximum?
5. What is the difference between local and absolute extrema?

Tip: When identifying local maxima and minima, always observe where the slope of the graph changes from positive to negative (maxima) or from negative to positive (minima).