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Multiple Derivatives Applet

Multiple Derivatives Applet
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2013-10-04 04:00
FunctionCalculusDerivative
This example demonstrates sketching functions and their multiple derivatives. It involves core math concepts like derivatives, turning points, extrema, and roots. Constructed using GeoGebra commands such as Random, Derivative, TurningPoint, Extremum, and Root. Suitable for high school and above students to learn and understand the properties of functions and their derivatives, ideal for calculus instruction.

GeoGebra Commands & Parameters

  1. Random(-3, 3) → D4
  2. Random(-1, 1) → A4
  3. Random(-5, 5) → E4
  4. Derivative(f) → f'
  5. Derivative(f') → f''
  6. TurningPoint(f) → A, B
  7. Extremum(f) → C, D, E
  8. Root(f') → F, G, H
  9. Extremum(f') → I, J
  10. Root(f'') → M, N
  11. TurningPoint(f') → K
  12. Extremum(f'') → L

AI Drawing Prompt Reference

Draw a function and its first and second derivatives, marking the turning points, extrema, and roots of the function, as well as the extrema and roots of the first derivative, and the turning points and extrema of the second derivative to illustrate the properties and relationships of the function and its derivatives.
The prompt above was compiled from the original drawing commands and is for reference only.