Absolute maximum

Definition

The absolute maximum of a function is the highest point over its entire domain. It represents the greatest output value that the function achieves.

5 Must Know Facts For Your Next Test

1. The absolute maximum can occur at critical points or endpoints of the domain.
2. To find an absolute maximum, evaluate the function at all critical points and endpoints.
3. A function can have only one absolute maximum value, but this value can occur at more than one point.
4. The first derivative test helps identify critical points where relative extrema might be found.
5. If a function is continuous on a closed interval, it will always have an absolute maximum.

Review Questions

• Where must you check to find the absolute maximum of a continuous function on a closed interval?
• Can an absolute maximum occur at more than one point in the domain? Explain your answer.
• How does the first derivative test assist in finding potential candidates for absolute maxima?

Related terms

Critical Point: A point in the domain of a function where its derivative is zero or undefined.

Relative Maximum: A point where a function's value is higher than all nearby points within some neighborhood.

First Derivative Test: \text{A method used to determine whether a critical point is a local minimum, local maximum, or neither by analyzing changes in sign of } f' (x).