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The problem asks for the interval where the function \( f \) is concave down. To solve this, we need to observe the graph for where the concavity of the function changes.

- **Concave Down** means the graph is curving downwards, like an upside-down bowl or hill. In other words, the second derivative \( f''(x) \) is negative in this region.
  
From the graph provided, the function appears to be concave down in the interval:

1. Starting from \( x = -6 \), the graph curves downward until around \( x = 0 \). 
2. At \( x = 0 \), the concavity changes and starts curving upwards (concave up) after this point.

Thus, the interval where \( f \) is concave down is \( (-6, 0) \), which corresponds to option **(C) (-6, 0)**.

Let me know if you need further clarification or details.

Here are some related questions:
1. What is concave up, and how does it differ from concave down?
2. How can you determine concavity from the second derivative \( f''(x) \)?
3. What happens to the concavity at inflection points?
4. What is the significance of the first derivative \( f'(x) \) in identifying concave intervals?
5. Can a function be concave up or down over its entire domain?

**Tip:** To find concavity, always check the sign of the second derivative. Negative indicates concave down, while positive indicates concave up.

Solve the graph analysis problem asking to identify the concave down interval of a function f. Learn how concavity is determined using the second derivative and observe how the graph behavior changes.

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