The answer was incorrect. I put them in as the answers but only DNE was correct for local minimums

I understand. It sounds like you were working with a problem involving local maximums and minimums, and the answer you submitted only correctly identified "DNE" (Does Not Exist) for the local minimums. Let's go over your approach and identify where the solution may have gone wrong.

1. **Could you share the full problem statement?** (e.g., the function you’re analyzing, any given interval, and other conditions).
2. **Did you calculate the first and second derivatives?** These are critical steps to determine critical points and whether they are maxima, minima, or points of inflection.
3. **Were there any specified points or boundaries?** Sometimes, problems also ask for evaluations at endpoints, which can influence the results if you're working within a closed interval.
  
If you could provide these details, I’ll guide you through a detailed solution.

Do you have any questions on this so far, or would you like a deeper explanation?

Here are some related questions to deepen understanding:

1. How do we find critical points of a function?
2. What is the significance of the second derivative in identifying local maxima and minima?
3. How can endpoints in a closed interval affect the existence of extrema?
4. Why might a function have no local minima but have local maxima?
5. What does the notation "DNE" signify in terms of calculus problems?

**Tip:** When analyzing functions, always check the first and second derivatives and consider whether the function is defined and continuous in the interval you’re analyzing.

The answer was incorrect. I put them in as the answers but only DNE was correct for local minimums.

This solution explores how to identify local maxima and minima in a function using critical points, first and second derivatives. Learn why only 'DNE' was correct for the local minimum and the importance of verifying answers with derivatives.

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