Can an endpoint be a local maximum?
Understand the Problem
The question is asking whether an endpoint of a function can be considered a local maximum. This relates to the concepts of calculus and optimization, specifically how local maxima are defined at the boundaries of the domain of a function.
Answer
An endpoint can be a local maximum.
An endpoint can be a local maximum if the function values close to the endpoint support this classification.
Answer for screen readers
An endpoint can be a local maximum if the function values close to the endpoint support this classification.
More Information
The classification of an endpoint as a local maximum depends on the function's behavior just inside the domain near the endpoint. If the function value at the endpoint is greater than the values of the function near it, it can be considered a local maximum.
Tips
A common mistake is confusing an endpoint's value being higher than values far away within the domain versus being higher than values immediately next to it.
Sources
- Can endpoints be local minimum? - Mathematics Stack Exchange - math.stackexchange.com
- Local Extrema: Endpoint Included? - Physics Forums - physicsforums.com
- Why can't relative extrema exist at endpoint in a function? - Quora - quora.com
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