The task is to determine the intervals where the function $f(x)$ is increasing, given the graph of its derivative $f'(x)$. To determine these intervals, we need to examine where $f'(x) > 0$, as this indicates that $f(x)$ is increasing.

Analysis of the Graph

1. Observing the graph of $y = f'(x)$, we see that $f'(x) > 0$ (above the x-axis) in the following intervals:

   • From $x \approx -6$ to $x \approx -3$.
   • From $x \approx 3$ to $x \approx 5$.

2. The intervals where $f'(x) > 0$ correspond to the intervals where $f(x)$ is increasing.

Answer

The intervals where $f(x)$ is increasing are: $(-6, -3) \quad \text{and} \quad (3, 5)$

So, the final answer is: $\text{Atsakymas: } (-6; -3) \text{ ir } (3; 5)$

Would you like further details on how to interpret derivative graphs or have any additional questions?

Related Questions

1. How can you identify the decreasing intervals for $f(x)$ based on $f'(x)$?
2. What does it mean if $f'(x)$ is zero at a point?
3. How would the concavity of $f(x)$ be determined from the second derivative, $f''(x)$?
4. What is the significance of critical points in the context of $f'(x) = 0$?
5. How can you sketch the original function $f(x)$ using information from $f'(x)$?

Tip

When analyzing graphs of derivatives, always focus on where the derivative is positive or negative to understand the behavior (increasing or decreasing) of the original function.