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Secant Approaching Tangent

Secant Approaching Tangent
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2016-08-15 02:59
CalculusDerivative
This example demonstrates how a secant line approaches a tangent line as Δt changes. Key concepts include secant lines, tangent lines, and derivatives. By adjusting the slider Δt, you can observe the secant line getting closer to the tangent line. This example uses functions, tangents, and slope commands in GeoGebra. Suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. Function((4.9 * x^(2)), 0, 5) → s
  2. Segment(P, Q) → a
  3. Line(A, P) → secant
  4. Tangent(P, s) → tangent
  5. Segment(Q, A) → b
  6. Slope(secant) → m_s
  7. Slope(tangent) → m_t

AI Drawing Prompt Reference

Draw a parabola opening upwards with the equation y=4.9x^2 from x=0 to x=5. Then, draw a secant line AP through a point P on the parabola, and draw the tangent line at point P. Finally, move point P to observe how the secant line approaches the tangent line.
The prompt above was compiled from the original drawing commands and is for reference only.