Rolle's Theorem

This calculus video tutorial provides a basic introduction into rolle's theorem. It contains plenty of examples and practice problems on how to find the value of c that will satisfy the conclusion of rolle's theorem on the closed interval [a, b]. For rolle's theorem to apply to a function, there are 3 conditions that must be met. (1) The function must be continuous on the closed interval [a, b]. (2) The function must be differentiable on the open interval (a, b). (3) f(a) = f(b). If these conditions are met, then f'(c)=0. There will be some number c in the interval [a, b] where a horizontal tangent line will exist. Derivative Applications - Formula Sheet: https://www.video-tutor.net/calculus-formula-sheets.html Final Exam and Test Prep Videos: https://bit.ly/41WNmI9 ___________________________ Introduction to Limits: https://www.youtube.com/watch?v=YNstP0ESndU Derivatives - Fast Review: https://www.youtube.com/watch?v=5yfh5cf4-0w Introduction to Related Rates: https://www.youtube.com/watch?v=I9mVUo-bhM8 _____________________________ Extreme Value Theorem: https://www.youtube.com/watch?v=Sx2lPZlnWfs Finding Critical Numbers: https://www.youtube.com/watch?v=Bp9EbV3COVA Local Maximum & Minimum: https://www.youtube.com/watch?v=WCq3sRzsJfs Absolute Extrema: https://www.youtube.com/watch?v=3wrXDw5ETh4 Rolle's Theorem: https://www.youtube.com/watch?v=LHym1ARc2cE ________________________________ Mean Value Theorem: https://www.youtube.com/watch?v=SL2RobwU_M4 Increasing and Decreasing Functions: https://www.youtube.com/watch?v=Dyl7jPlJXOM First Derivative Test: https://www.youtube.com/watch?v=G5wlKltW7pM Concavity & Inflection Points: https://www.youtube.com/watch?v=OhqNbQi9QPk Second Derivative Test: https://www.youtube.com/watch?v=G8GAsYkZlpE _________________________________ L'Hopital's Rule: https://www.youtube.com/watch?v=Gh48aOvWcxw Curve Sketching With Derivatives: https://www.youtube.com/watch?v=JTVNUdL7sWs Newton's Method: https://www.youtube.com/watch?v=-5e2cULI3H8 Optimization Problems: https://www.youtube.com/watch?v=lx8RcYcYVuU _______________________________________ Final Exams and Video Playlists: https://www.video-tutor.net/ Full-Length Videos and Worksheets: https://www.patreon.com/MathScienceTutor/collections