The task asks to determine all intervals on which the graph of $f$ is decreasing.

Steps to determine where the graph is decreasing:

1. Identify the critical points: These are the points where the slope of the graph is zero (horizontal tangent lines), which occur at local maxima and minima.
2. Look at the behavior of the graph: After identifying the critical points, determine where the graph is sloping downward. This will occur between the points where the graph transitions from a maximum to a minimum.

From the graph:

• The graph starts decreasing just after the maximum at $x = -6$ and continues decreasing until the minimum at $x = -2$.
• The graph starts decreasing again after the maximum at $x = 3$ and continues decreasing until $x = 6$.

Decreasing intervals:

• The function is decreasing on the intervals $(-6, -2)$ and $(3, 6)$.

Thus, the intervals where the graph of $f$ is decreasing are: $(-6, -2) \cup (3, 6)$

Would you like further details on the process or have any other questions?

Here are five related questions you might want to explore:

1. How do you find critical points using derivatives?
2. What is the relationship between the first derivative and increasing/decreasing behavior?
3. How do local maxima and minima relate to the intervals of increase or decrease?
4. What happens if the graph is flat over an interval? Is it increasing, decreasing, or constant?
5. How do you apply the second derivative to analyze concavity?

Tip: When analyzing a graph, always start by identifying where the slope changes direction. This will guide you in determining the intervals of increase and decrease.