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Slippery Slopes: Deriving the Derivative by magness.erin

Slippery Slopes: Deriving the Derivative by magness.erin
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2014-06-30 23:21
Coordinate GeometryDerivativeGraphing
This example demonstrates the geometric meaning of derivatives by comparing the graphs of the original function and its derivative. Core math concepts include derivatives, intersections, differential equations, and similarity transformations. It uses GeoGebra objects C, B, A, a, b, c in its construction. Suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. C(x) = (1 / 3 * x^(3)) - (9 * x) + 3
  2. Conic B
  3. Line A(-1.0, 1.0, 0.0)
  4. Boolean a(true)
  5. Boolean b(true)
  6. Boolean c(true)

AI Drawing Prompt Reference

Draw the graph of the cubic function y = (1/3)x^3 - 9x + 3, then draw its derivative graph. Use the line y = x - 8 as a reference line to observe the intersection points between the function graph and the derivative graph. Adjust the three boolean switches to show or hide these intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.