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Sketching a Derivative

Sketching a Derivative
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2020-09-21 06:17
CalculusDerivativeGraphing
In collections Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function based on its graph. The core math concepts involved are the geometric meaning of derivatives, which represent the slope of tangents to the original function's graph at various points. Key GeoGebra commands and objects used in the construction include f (function), f' (derivative), a (point), A (point), g (object), B (point), h (object), and b (point). It is suitable for high school and introductory university students learning about derivatives and their graphical relationships.

GeoGebra Commands & Parameters

  1. f(x) = x^(3) / 3
  2. f'(x) = f'(x)
  3. Numeric a(-7)
  4. (a, f(a))
  5. g(x) = If[a - 1 ≤ x ≤ a + 1, f(a) + (f'(a) * (x - a))]
  6. (a, f'(a))
  7. f'(x)
  8. Boolean b(false)

AI Drawing Prompt Reference

Draw a graph showing the original function and its derivative. Include a point on the original function with its derivative value labeled. Also, draw a local linear approximation based on the function and derivative near that point. Ensure the graph is clear and labeled to help understand the geometric meaning of the derivative.
The prompt above was compiled from the original drawing commands and is for reference only.