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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?

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### 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.

Nubrėžtas funkcijos y = f(x) (Df = [-7; 5]) išvestinės grafikas. Nustatyk funkcijos f(x) didėjimo intervalus.

Find the intervals where the function f(x) is increasing based on the graph of its derivative f'(x) over the interval [-7, 5]. This calculus problem covers concepts related to derivatives and increasing functions, suitable for students in Grades 11-12.

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