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To solve this problem, we need to analyze the graph and determine the relative values of the derivatives \( f'(-4) \), \( f'(-2) \), \( f'(0) \), \( f'(2) \), and \( f'(4) \).

### Approach:
1. **Understanding the graph**: The graph shows the function \( f(x) \). The derivative values at specific points tell us the slope of the tangent line at those points.
   
2. **Find slopes at specific points**:
   - \( f'(-4) \): At \( x = -4 \), the slope appears to be positive since the line is increasing.
   - \( f'(-2) \): At \( x = -2 \), the graph is a peak, meaning the slope is zero here because it's a local maximum.
   - \( f'(0) \): At \( x = 0 \), the graph is flat (horizontal), meaning the slope is zero again.
   - \( f'(2) \): At \( x = 2 \), the graph is still increasing but flatter than at \( x = -4 \). The slope is slightly positive.
   - \( f'(4) \): At \( x = 4 \), the graph is decreasing sharply, so the slope is negative.

### Comparing the slopes:

- \( f'(-4) \): Positive and relatively steep.
- \( f'(-2) \): Zero (local maximum).
- \( f'(0) \): Zero (flat section).
- \( f'(2) \): Positive but not as steep as at \( x = -4 \).
- \( f'(4) \): Negative and quite steep.

### Ordering from least to greatest:

- The smallest slope is \( f'(4) \) (negative value).
- Then we have \( f'(-2) \) and \( f'(0) \), both equal to zero.
- Next is \( f'(2) \), a positive slope, but not as steep.
- Finally, the largest slope is \( f'(-4) \), which is the steepest positive slope.

Thus, the order is:
\[ f'(4) < f'(-2) = f'(0) < f'(2) < f'(-4) \]

Let me know if you need any further clarification or details!

Here are five related questions you could explore:
1. What is the definition of the derivative and how does it relate to the slope of a graph?
2. What are critical points, and why do they occur at \( x = -2 \) and \( x = 0 \) on this graph?
3. How do you interpret increasing and decreasing intervals from a graph of a function?
4. How can you determine concavity from the graph of a function, and what does it say about the second derivative?
5. What is the significance of points where the derivative equals zero?

**Tip:** The derivative gives you the rate of change of a function. When analyzing graphs, local maximum and minimum points often correspond to where the derivative is zero, meaning the slope is flat.

Based on the graph, order the given values of the derivatives f'(-4), f'(-2), f'(0), f'(2), and f'(4) from least to greatest.

Learn how to order the values of the derivatives f'(-4), f'(-2), f'(0), f'(2), and f'(4) by analyzing the graph of a function. This problem focuses on understanding the slopes of the tangent lines and determining the relative order of the derivatives at specific points.

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