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The question is asking for the maximum value of \( \sqrt{x} \) on the interval \( I = (1, 4) \).

### Solution:

The function given is \( f(x) = \sqrt{x} \), which is defined and continuous for \( x \geq 0 \).

1. **Domain of the interval**: The interval is \( I = (1, 4) \), which means the interval includes numbers from slightly greater than 1 up to 4, but does not include the endpoints 1 and 4.
  
2. **Behavior of \( f(x) \)**:
   - At \( x = 1 \), \( \sqrt{1} = 1 \).
   - At \( x = 4 \), \( \sqrt{4} = 2 \).

   The function \( \sqrt{x} \) is an increasing function in the domain \( x \geq 0 \). Therefore, as \( x \) approaches the upper bound of the interval (4), the function will reach its maximum value.

3. **Maximum value**:
   Since \( x = 4 \) is at the boundary of the interval and the function increases as \( x \) increases, the maximum value of \( \sqrt{x} \) on this interval is \( \sqrt{4} = 2 \).

Thus, the maximum value of \( \sqrt{x} \) on the interval \( I = (1, 4) \) is **2**, which corresponds to option **e**.

Would you like more details on the reasoning behind this, or any specific part explained further?

### Related Questions:
1. What is the derivative of \( \sqrt{x} \), and how does it confirm the increasing nature of the function?
2. How would the answer change if the interval were closed \( [1, 4] \)?
3. Can \( f(x) = \sqrt{x} \) have a minimum on the interval \( (1, 4) \)?
4. What is the difference between open and closed intervals in finding extrema?
5. How would the maximum change if the interval was \( (0, 4) \)?

### Tip:
Always check if the interval is open or closed when finding maximum or minimum values, as it affects whether you can include the endpoints in your calculation.

Nilai maksimum dari \( \sqrt{x} \) pada selang \( I = (1, 4) \) adalah?

This problem asks for the maximum value of the square root function \( \sqrt{x} \) on the interval \( I = (1, 4) \). The solution involves understanding the behavior of square root functions on open intervals and finding the maximum value.

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