Rolle’s Theorem and the Mean Value Theorem | AP Calculus AB

Worked examples, fresh practice, captions, and corrected transcript: https://calculus.mrwittman.com/10-23-... Connect extrema and theorem hypotheses, prove and apply Rolle’s Theorem, interpret parallel secants and tangents through the Mean Value Theorem, and explain a truck’s speed from its travel time. Chapters 0:00 Review: extrema and critical inputs 2:28 The Extreme Value Theorem 3:07 The Intermediate Value Theorem 5:38 Hypotheses and conclusions 6:33 Rolle’s three hypotheses 8:55 Prove Rolle’s Theorem using extrema 12:54 The constant-function case 14:55 Rolle’s Theorem: a cube-root example 16:53 An endpoint derivative can be undefined 17:52 All three hypotheses are satisfied 18:33 Solve the zero-derivative equation 20:40 Choose the interior value of c 22:17 The Mean Value Theorem 23:29 Parallel tangent and secant lines 26:27 Average and instantaneous rates 28:08 A truck between two radar observations 29:45 Compute and convert the average rate 31:38 Check the motion-model hypotheses 32:29 A guaranteed instant at 75 mph Course: AP Calculus AB Recorded October 23, 2026