https://file.aiquickdraw.com/mathbot/file/1728202434573yga5emcu.jpg

Based on the provided image, we need to determine on which interval the function is monotonically increasing.

First, let’s translate the question:

"Berdasarkan gambar di atas pada interval \([E_1, C_1]\), pada interval manakah fungsi tersebut monoton naik?" translates to "Based on the graph above, within the interval \([E_1, C_1]\), in which interval is the function monotonically increasing?"

To solve this, we will analyze the graph:

1. **Identifying the intervals**: 
   - \(B_1\) to \(J_1\)
   - \(C_1\) to \(B_1\)
   - \(D_1\) to \(C_1\)
   - \(E_1\) to \(D_1\)

2. **Analyzing the graph**:
   - The function increases when moving from left to right if the slope of the curve is positive.

By observing the graph:
- The interval \([B_1, J_1]\) shows a decreasing function initially.
- The interval \([C_1, B_1]\) shows a decreasing trend.
- The interval \([D_1, C_1]\) shows the function increasing from \(D_1\) to \(C_1\).
- The interval \([E_1, D_1]\) shows the function decreasing from \(E_1\) to \(D_1\).

**Conclusion**: The interval where the function is monotonically increasing is \([D_1, C_1]\).

Therefore, the correct answer is:

**c. \([D_1, C_1]\)**

Do you want details or have any questions? 

Here are 5 related questions for further understanding:

1. What does it mean for a function to be monotonically increasing?
2. How can you determine if a function is increasing or decreasing over an interval from its derivative?
3. What are the characteristics of a function that has local maxima and minima?
4. How do you find the intervals of increase and decrease for a given function?
5. How can the first derivative test be used to determine the nature of critical points?

**Tip:** When analyzing graphs, always look for the points where the slope changes to identify increasing and decreasing intervals.

Berdasarkan gambar di atas pada interval [E_1, C_1], pada interval manakah fungsi tersebut monoton naik?

Learn how to identify intervals of monotonic increase on a graph. This problem focuses on analyzing the curve behavior, understanding where the slope is positive, and applying the Monotonicity Theorem.

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