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.