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Derivative at a Point by Anthony OR 柯志明

Derivative at a Point by Anthony OR 柯志明
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2015-04-17 18:25
FunctionCalculusDerivativeGeometric ConstructionGraphing
This example demonstrates the magnified view of a function's graph and its tangent line at a movable point, focusing on understanding derivatives and tangents. It involves core math concepts like derivatives, tangents, angles, and function graphs. Constructed using GeoGebra commands/objects such as Point, Tangent, Polygon, Segment, and Line. Suitable for high school calculus instruction or student exploration of initial differential concepts.

GeoGebra Commands & Parameters

  1. Point(xAxis) → F
  2. Tangent(A, f) → a
  3. Polygon(B, C, 4) → poly1, b, c, d, e, D, E
  4. Point(xAxis) → G
  5. Segment(F, A) → g
  6. Segment(G, H) → h
  7. Line(A, H) → j

AI Drawing Prompt Reference

Draw a function graph with a movable point on it, and show the tangent line at that point. Zoom in to clearly display the local relationship between the tangent line and the function graph, including the point and line segment forming the tangent, and a quadrilateral highlighting the angle formed by the tangent and coordinate axes.
The prompt above was compiled from the original drawing commands and is for reference only.