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The question asks for the correct definition of a local minimum of a function.

### Explanation:
- A **local minimum** refers to a point where the function attains its smallest value within a particular interval (not necessarily the smallest value across the entire domain of the function).
- It means that at the local minimum, the function value is smaller than all nearby points, but not necessarily smaller than the function's values elsewhere in the entire domain.

### Correct Answer:
- **A) smallest value for a given interval.**

Would you like more details on local minimums or maxima?

### Related Questions:
1. What is the difference between a local minimum and a global minimum?
2. Can a function have more than one local minimum?
3. How can you determine if a point is a local minimum using the first or second derivative?
4. What is the graphical interpretation of a local minimum?
5. How does the concept of local maximum differ from local minimum?

### Tip:
When using the first derivative test, a local minimum occurs where the derivative changes from negative to positive.

A local minimum of a function is its: A) smallest value for a given interval. B) smallest value of the function over its entire domain. C) largest value for a given interval. D) largest value of the function over its entire domain.

Explore the concept of a local minimum in functions. Learn how to identify the smallest value of a function within a given interval, using derivative tests for precise function analysis. Suitable for Grades 10-12.

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