Overview
The mean value theorem tells us (roughly) that if we know the slope of the secant line of a function whose derivative is continuous, then there must be a tangent line nearby with that same slope. This lets us draw conclusions about the behavior of a function based on knowledge of its derivative.
Lecture Video and Notes
Video Excerpts
» Clip 1: Description of the Mean Value Theorem (00:11:00)
From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006
Clip 1: Description of the Mean Value Theorem
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» Clip 2: Consequences of the Mean Value Theorem (00:08:00)
From Lecture 14 of 18.01 Single Variable Calculus, Fall 2006
Clip 2: Consequences of the Mean Value Theorem
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Recitation Video
Increasing or Decreasing
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Worked Example
Generalizing the Mean Value Theorem