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References: Mean Value Theorem and Extrema

  1. Mean value theorem - Wikipedia - Statement, proof, geometric interpretation, and consequences of the MVT. Core reference for the theorem that connects average and instantaneous rates of change.

  2. Rolle's theorem - Wikipedia - The special case of the MVT where f(a) = f(b), with proof and applications. Directly supports the chapter's progression from Rolle's theorem to the full MVT.

  3. Extreme value theorem - Wikipedia - Guarantees existence of absolute extrema on closed intervals, with proof and relationship to continuity. Foundation for the optimization framework in this chapter.

  4. Calculus: Early Transcendentals (9th Edition) - James Stewart - Cengage Learning - Sections 4.1-4.2 cover absolute and local extrema, Fermat's theorem, the closed interval method, and the Mean Value Theorem.

  5. Thomas' Calculus (15th Edition) - Joel Hass, Christopher Heil, Maurice Weir - Pearson - Sections 4.1-4.2 provide clear statements of the EVT, Fermat's theorem, and MVT with excellent geometric illustrations.

  6. Mean Value Theorem - Paul's Online Math Notes - Worked examples finding the value of c guaranteed by the MVT, with geometric explanations and applications.

  7. Extreme Value Theorem and Critical Points - Khan Academy - Interactive lessons on finding absolute extrema using the closed interval method, aligned to AP curriculum.

  8. Mean Value Theorem Explained - Professor Leonard - Detailed lecture covering Rolle's theorem and MVT with geometric motivation and worked examples.

  9. Extreme Values of Functions - Math is Fun - Visual introduction to finding maximum and minimum values with interactive graphs showing critical points and endpoints.

  10. Mean Value Theorem - Whitman College Calculus - Open-source section with the MVT statement, proof, applications to monotonicity, and exercises.