Understanding Derivatives through Secant Lines
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This example dynamically demonstrates how the slope of a secant line approaches the slope of a tangent line, visually illustrating the geometric meaning of a derivative. Key math concepts include the definition of a derivative, secant lines, tangent lines, and slopes. GeoGebra commands and objects used in construction are Point, Line, Segment, Corner, Tangent, Slope, OrthogonalLine, Intersect, Polygon. Suitable for high school calculus instruction to help students grasp the concept of derivatives.
GeoGebra Commands & Parameters
Point(xAxis) → APoint(xAxis) → BLine(Af, Bf) → gSegment(Bf, B) → hSegment(Af, A) → iCorner(1, 1) → C1Corner(1, 2) → C2Corner(1, 3) → C3Corner(1, 4) → C4Tangent(Af, f) → jSlope(j) → mSlope(g) → m_1OrthogonalLine(Afl, xAxis) → kIntersect(k, j) → CIntersect(g, k) → DPolygon(Af, Afl, C) → t1, c, af, aflPolygon(Af, Afl, D) → t2, l, n, p