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Derivative as the Gradient Function

Derivative as the Gradient Function
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2015-02-03 10:43
CalculusDerivativeLimit
This example explains the concept of derivative by showing the limit value of the slope of the chord on a curve. Key math concepts include derivative and limit. It uses GeoGebra commands such as Point, Segment, OrthogonalLine, Intersect, and Slope. Suitable for high school math education, aiding students in understanding the geometric meaning of derivatives.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Segment(B, A) → a
  3. OrthogonalLine(A, xAxis) → b
  4. OrthogonalLine(B, yAxis) → c
  5. Intersect(b, c) → C
  6. Segment(A, C) → d
  7. Segment(B, C) → e
  8. Slope(a) → g

AI Drawing Prompt Reference

Draw a curve and place two points on it, one fixed and the other movable. Connect these two points with a chord. From the fixed point, draw a line perpendicular to the horizontal axis, and from the movable point, draw a line perpendicular to the vertical axis; these two perpendicular lines intersect at a point. Connect this intersection point to both original points with segments, forming a right triangle. Finally, display the slope of the chord, which changes as the movable point slides, illustrating the geometric meaning of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.