To determine where the function $f(x)$ is increasing or decreasing based on the graph of its derivative $f'(x)$, we analyze the sign of $f'(x)$:

• When $f'(x) > 0$: $f(x)$ is increasing.
• When $f'(x) < 0$: $f(x)$ is decreasing.

Analysis:

1. Increasing intervals: The graph of $f'(x)$ is above the $x$-axis on the interval $(3, 4)$. Hence, $f(x)$ is increasing on $(3, 4)$.

2. Decreasing intervals: The graph of $f'(x)$ is below the $x$-axis on the intervals $(0, 2)$ and $(4, 6)$. Therefore, $f(x)$ is decreasing on $(0, 2) \cup (4, 6)$.

Final Answer:

• $f(x)$ is increasing on $(3, 4)$.
• $f(x)$ is decreasing on $(0, 2) \cup (4, 6)$.

Let me know if you need further clarification! Here are 5 related questions to expand your understanding:

1. What happens to $f(x)$ at points where $f'(x) = 0$?
2. How can the second derivative $f''(x)$ help analyze the concavity of $f(x)$?
3. What are the critical points of $f(x)$ based on $f'(x)$?
4. How would the intervals change if $f'(x)$ crossed the $x$-axis more frequently?
5. What do changes in the steepness of $f'(x)$ indicate about the behavior of $f(x)$?

Tip: Always check where $f'(x)$ changes sign to locate critical points and determine increasing/decreasing behavior!