MathPlotAI Logo MathPlotAI

Newton's Method by Dr. Doug Davis, 3D

Newton's Method by Dr. Doug Davis, 3D
Loading the math board and drawing, please wait…
2016-05-17 22:49
FunctionCalculusDerivative
This example demonstrates Newton's Method through two GeoGebra applets. The first applet derives the method, while the second (by Paul Regan) illustrates the method with examples. The example involves the core concept of derivatives and uses GeoGebra commands such as ConstructionStep, Segment, Vector, and Tangent from the construction summary. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. ConstructionStep() → c
  2. Segment(A, B) → a
  3. Vector(E, F) → u
  4. Tangent(B, f) → b
  5. Vector(G, H) → v
  6. Intersect(b, xAxis) → C
  7. Vector(A, C) → d
  8. Vector(I, C) → w

AI Drawing Prompt Reference

Draw a 3D coordinate system illustrating Newton's method. Start with a curve representing a function. Pick a point on the curve, draw a tangent line at that point, and extend it to intersect the x-axis. From that intersection, draw a vertical or slanted segment back to the curve, marking the next point. Repeat this process to show successive approximations. Include labeled points for the initial guess, tangent points, x-axis intersections, and directed vectors connecting them. Emphasize the tangent-curve contact and the iterative path toward the root.
The prompt above was compiled from the original drawing commands and is for reference only.