Mean value theorems compared

This animated video illustrates the evolutionary relationship among three fundamental Mean Value Theorems: Cauchy's, Lagrange's, and Rolle's. It begins by presenting Cauchy's theorem from a parametric curve perspective, then derives Lagrange's theorem as a specific case when $g(t)=t$, and finally simplifies it further into Rolle's theorem under the condition $f(a)=f(b)$. A concluding flowchart summarizes the logical progression from general principles to special cases.

Before you watch

• Geometric meaning of derivatives
• Basics of parametric equations
• Distinction between continuity and differentiability