The image shows the graph of $f'$, the derivative of a function $f$, and the task is to determine whether $f$ is increasing or decreasing for certain intervals based on the sign of $f'$.

To do this, we need to recall that:

• When $f'(x) > 0$, the function $f(x)$ is increasing.
• When $f'(x) < 0$, the function $f(x)$ is decreasing.

Let's break down the intervals:

1. Interval $0 < x < x_1$:
   Look at the graph of $f'$ in this region. If $f' > 0$, then $f$ is increasing; if $f' < 0$, then $f$ is decreasing.

2. Interval $x_1 < x < x_2$:
   Same logic. Analyze the sign of $f'$ between $x_1$ and $x_2$.

3. Interval $x_2 < x < x_3$:
   Similarly, observe whether $f'$ is positive or negative here.

4. Interval $x_3 < x < x_4$:
   Analyze the sign of $f'$ in this interval.

5. Interval $x_4 < x < x_5$:
   Finally, look at the graph in this region to see if $f'$ is above or below the x-axis.

Let me know if you need a more detailed breakdown for each interval or if you'd like help with filling in the specific values.