Absolute minimum

Definition

The absolute minimum of a function is the lowest point over its entire domain. It represents the smallest value that the function can take.

5 Must Know Facts For Your Next Test

1. The absolute minimum is also known as the global minimum.
2. It can occur at endpoints or critical points of a function.
3. To find it, evaluate the function at critical points and endpoints, then compare values.
4. A function may have an absolute minimum even if it does not have an absolute maximum.
5. In calculus, finding an absolute minimum often involves using derivatives to locate critical points.

Review Questions

• What steps are involved in finding the absolute minimum of a function?
• Can a function have more than one absolute minimum? Why or why not?
• How do you determine if a critical point is an absolute minimum?

Related terms

Critical Point: A point on a graph where the derivative is zero or undefined.

Endpoint: Points at the ends of an interval where a function is defined.

Absolute Maximum: The highest point over the entire domain of a function.