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Slope of a Curve by Dr. Doug Davis, 3D

Slope of a Curve by Dr. Doug Davis, 3D
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2015-12-30 05:51
FunctionCalculusDerivative
In collections Fun with Functions
This applet demonstrates how the slope of the secant line approaches the slope of the curve. By adjusting the position of points, the left, right, and centered convergence can be observed. The applet involves the core concept of derivatives and uses GeoGebra objects such as polynomials, segments, and tangents for construction. Suitable for high school mathematics education and learning calculus concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → K
  2. Intersect(xAxis, yAxis) → A
  3. Polynomial({A, C, D, E, F}) → f
  4. Segment(G, B) → a
  5. Slope(a) → m
  6. Polygon(G, H, B) → poly1, b, g_1, h_1
  7. Midpoint(b) → I
  8. Midpoint(g_1) → J
  9. Line(G, B) → c
  10. OrthogonalLine(K, xAxis) → i
  11. Locus(m_{secant}, h) → loc1
  12. Intersect(g, i, (2, 1.0445050366565525)) → N
  13. Tangent(N, g) → k
  14. Slope(k) → m_1
  15. Defined(m) → defined