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Definition of the Derivative

Definition of the Derivative
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2019-12-06 21:31
CalculusDerivativeLimit
This example illustrates the definition of the derivative through the slope of the tangent line. Key mathematical concepts include derivatives, limits, and tangents. It utilizes GeoGebra commands such as Point, OrthogonalLine, Intersect, Segment, and Line. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(f) → P
  2. Point(f) → B
  3. OrthogonalLine(P, xAxis) → h
  4. OrthogonalLine(B, xAxis) → i
  5. Intersect(h, xAxis) → C
  6. Intersect(i, xAxis) → D
  7. Segment(C, D) → j
  8. Point(j) → E
  9. OrthogonalLine(E, j) → k
  10. Intersect(f, k, 1) → Q
  11. Line(P, Q) → g
  12. Segment(E, C) → l
  13. Point(xAxis) → A
  14. Segment(E, A) → m
  15. Point(m) → F

AI Drawing Prompt Reference

Draw a function curve, take two points on it, draw perpendicular lines to the x-axis, connect the feet of the perpendiculars, then draw a perpendicular line at the midpoint of the connection to the function curve, which intersects the curve at a point. Connect the original point and this intersection point to show the tangent line. Also, draw a perpendicular line from the intersection point to the x-axis and take a point on this line, connecting the intersection point and this point to form another auxiliary line segment.
The prompt above was compiled from the original drawing commands and is for reference only.