It seems you have concerns about local maxima. Could you provide more context or details about the specific problem or function you're dealing with? This will help me assist you better.

Here are five related questions to consider:

1. What function are you analyzing for local maxima?
2. How are you currently identifying local maxima (e.g., derivative tests, graphing)?
3. Have you checked for critical points and their nature?
4. Are you considering endpoints if the function is defined on a closed interval?
5. Would you like to explore specific examples or cases where local maxima might be incorrectly identified?

Tip: When looking for local maxima, ensure you're checking both the first and second derivatives for accurate identification.