Rolle's Theorem: Statement, Intuition and Proof! | Real Analysis Intro

We explain what Rolle's Theorem in calculus is, what is the visual intuition and motivation behind it, how to prove it rigorously, and why it fails if we omit any of the hypotheses, all from scratch in a video under 20 minutes! The concepts and ideas in this video are fundamental in calculus and extremely helpful for doing well on homework, assignments, tests and exams in high school and college math (including AP Calculus in the USA). In the course of the video, we also discuss the extreme value theorem, the left-hand and right-hand derivatives at a point, the concept of local/global maxima/minima, and how to rigorously write down and think intuitively about a mathematical proof! If you enjoy the content on my channel, I would love if you could please like ✅ , subscribe 🎉, and share ⏩ with students, classmates, friends and family - it means so much to help support me in my goal of creating *elite infinite free accessible* math education worldwide! 😊 If you would like to support my channel and my long-term vision of changing lives through math education beyond this (which of course would mean so much to me 🤗), please check out my "Buy me a Coffee" and my "Patreon" page! (If I have provided value to you through my free videos, any level of contribution is appreciated!) Buy me a Hot Chocolate 😊: https://buymeacoffee.com/math_mastery_with_amitesh ☕️ Become a Patreon Member 🤩: https://patreon.com/MathMasterywithAmitesh