MathPlotAI Logo MathPlotAI

Derivative as Locus

Derivative as Locus
Loading the math board and drawing, please wait…
2015-11-04 21:05
Coordinate GeometryCalculusDerivativeParametric EquationLocus
This example demonstrates the locus formed by the slope of tangents at points moving along a function graph, illustrating the geometric meaning of derivatives, parametric curves, and coordinate geometry. It uses GeoGebra commands like Point, Tangent, Slope, and Locus with objects such as f (function), A (point), a (parameter), b (parameter), B (point), and loc1. Suitable for high school and above students studying calculus, parametric equations, and function graph properties.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Tangent(A, f) → a
  3. Slope(a) → b
  4. Locus(B, A) → loc1

AI Drawing Prompt Reference

Draw a function graph, then move a point A on the graph to draw a tangent line a at point A, mark the slope b of the tangent line, and finally create a locus loc1 by tracing point A.
The prompt above was compiled from the original drawing commands and is for reference only.