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.