Rolle's Theorem: Statement, Geometric Meaning, and Proof | Calculus Craze

Описание: In this lecture, Abdul Fatah Khalil Rajri from Calculus Craze explains one of the most fundamental results in calculus: Rolle's Theorem.

We go beyond just memorizing the formula. We dive deep into the three necessary conditions (Continuity, Differentiability, and Equal Endpoints) and provide a rigorous formal proof using the Extreme Value Theorem and Fermat's Theorem (Interior Extremum Theorem).

What we cover in this video:

The 3 conditions for Rolle's Theorem to apply.

The geometric interpretation (Why there must be a horizontal tangent).

A complete mathematical proof for both constant and non-constant functions.

Practical examples of where Rolle's Theorem is used.

Recommended Video: If you haven't seen our proof of the Interior Extremum Theorem, watch it here:    • Why Derivatives are Zero at Local Extrema?...  

Timestamps: 0:00 - Introduction to Rolle's Theorem 1:15 - The 3 Essential Conditions 3:30 - Geometric Intuition 5:45 - Formal Proof (Case by Case) 11:00 - Conclusion & Recap

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