Visualizing Derivative Definition: Secant Line Approaching Tangent Line

This example demonstrates the geometric definition of the derivative through dynamic visualization. What it shows: As a point moves along a function curve, the secant line gradually approaches the tangent line. Core concepts: limit definition of derivative, relationship between secant and tangent lines, concept of limits. Construction: Uses Point commands to create moving point P and fixed point B, Line/Segment commands to draw secant PB and tangent, Intersect to find curve intersections with axes, OrthogonalLine for perpendiculars, with text labels for key information. Suitable for high school mathematics or introductory college calculus, serving as an intuitive teaching tool when introducing the derivative concept.