How the concept of local linearity defines the derivative
In short: To understand calculus, you must first understand how curves behave when you zoom in. This video explores the fundamental link between local linearity and differentiability using interactive graphing tools.
The video uses the Desmos graphing calculator to provide an intuition for how local linearity relates to differentiability. By observing functions at a microscopic scale, students can see how complex curves begin to resemble straight lines.
This concept is a cornerstone of AP Calculus AB. The lesson was developed by Bill Scott, a teacher at Phillips Academy in Andover, Massachusetts, which was one of the first schools to offer AP courses nearly 60 years ago.
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Sources
- Summary by Intellect · source: Local linearity and differentiability | Derivatives introduction | AP Calculus AB | Khan Academy
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