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The problem asks which condition is true if a function \( f(x) \) is **decreasing** in the interval \( (a; b) \).

### Explanation:
- A function is decreasing on an interval when its **derivative** is **negative** in that interval.
- Mathematically, this means \( f'(x) < 0 \) on \( (a; b) \).
  
### Correct Answer:
The correct option is **(e)**: \( f'(x) < 0 \) en ese intervalo.

Would you like further clarification on the reasoning or any related concepts?

### 5 Related Questions:
1. What does it mean if \( f'(x) = 0 \) in an interval?
2. How can you determine if a function is increasing using its derivative?
3. What role does the second derivative \( f''(x) \) play in analyzing a function's concavity?
4. How do critical points relate to increasing or decreasing intervals of a function?
5. What is the significance of the sign of \( f'(x) \) in determining extrema (maxima or minima)?

### Tip:
The derivative provides key information about the function's behavior—whether it's increasing, decreasing, or constant at various intervals.

Si una función f(x) decrece en un (a ; b) , entonces:

Learn how to determine if a function is decreasing over an interval by analyzing its derivative. This problem explains how f'(x) < 0 indicates a decreasing function in the interval (a, b). Suitable for high school students studying calculus.

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