https://file.aiquickdraw.com/mathbot/file/17267167839897vm1t21b.jpg

Let's analyze the graph to correctly answer the questions based on the local maxima and minima, as well as the increasing and decreasing intervals.

### (a) Local Maxima and Minima

#### Estimating from the graph:

1. **Left-most local maximum:**
   - The first peak occurs around \(x = -2\) and \(y \approx 1\).
   - So the left-most local maximum is at **(-2, 1)**.

2. **Next local maximum:**
   - The next peak is around \(x = 2\), and \(y = 2\).
   - So the next local maximum is at **(2, 2)**.

3. **Left-most local minimum:**
   - The first valley occurs around \(x = -1\), and \(y \approx -1\).
   - So the left-most local minimum is at **(-1, -1)**.

4. **Next local minimum:**
   - The next valley is at \(x = 1\), and \(y \approx -1\).
   - So the next local minimum is at **(1, -1)**.

### (b) Intervals of Increase and Decrease

#### Increasing intervals:
- The graph increases in two sections:
  1. From \(x \approx -3\) to \(x = -2\).
  2. From \(x = 0\) to \(x = 2\).
  
  Hence, the increasing intervals are: **\((-3, -2) \cup (0, 2)\)**.

#### Decreasing intervals:
- The graph decreases in three sections:
  1. From \(x = -\infty\) to \(x = -3\).
  2. From \(x = -2\) to \(x = 0\).
  3. From \(x = 2\) to \(x = \infty\).

  Hence, the decreasing intervals are: **\((- \infty, -3) \cup (-2, 0) \cup (2, \infty)\)**.

### Final Answers:

- (a) Local maximums and minimums:
  - Left-most local maximum: \((-2, 1)\)
  - Next local maximum: \((2, 2)\)
  - Left-most local minimum: \((-1, -1)\)
  - Next local minimum: \((1, -1)\)

- (b) Increasing: \((-3, -2) \cup (0, 2)\)
- Decreasing: \((- \infty, -3) \cup (-2, 0) \cup (2, \infty)\)

Would you like further clarifications or a detailed explanation on any of these? 

Here are 5 follow-up questions you might find useful:
1. How do you define a local maximum and minimum on a graph?
2. What is the difference between a global maximum and a local maximum?
3. How do you determine increasing and decreasing intervals using the derivative?
4. How would these answers change if the function were different?
5. Can a graph have no local maximum or minimum?

**Tip:** Always observe where the graph changes direction to determine local extrema and intervals of increase or decrease.

The graph of a function is given. Use the graph to estimate the local maximum and minimum values, and find the intervals where the function is increasing and decreasing.

Learn how to estimate local maxima and minima and determine intervals of increasing and decreasing behavior from a graph. This problem is ideal for students learning basic calculus concepts, including local extrema and the behavior of functions.

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