



How do removable, jump, and essential discontinuities affect the theorem?
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what is the extreme value theorem Informational
- Discuss its relevance to optimal control. How does the Extreme Value Theorem connect to the idea of a Whitney embedding theorem in differential topology?
- How can the Extreme Value Theorem help find optimal solutions?
- Does it play a role in the study of convergence?
- Explain the connection to Whitney embeddings. What are some examples of functions defined on unbounded closed sets where absolute extrema exist?
- Explain the significance of continuous functions in the Extreme Value Theorem. What does the Extreme Value Theorem guarantee?
- Define the points where the derivative is zero or undefined.
- Illustrate with examples. How can the Extreme Value Theorem be used to find the maximum and minimum values of polynomial functions on closed intervals?
- How does it help determine the range of a function?
- Discuss its topological significance. What are some common pitfalls to avoid when applying the Extreme Value Theorem in problem-solving?
- Discuss its significance in calculus. How does the Extreme Value Theorem relate to the concept of optimization?
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