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Derivative Graphing Example

Derivative Graphing Example
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2020-09-21 07:02
FunctionCalculusDerivativeGraphing
In collections Sketching Derivatives
This example demonstrates how to sketch the derivative of a given function. The key mathematical concepts involve the geometric meaning and calculation of derivatives. Construction involves using GeoGebra commands such as c, f, f', a, A, B, h, b, g. Suitable for high school students or college freshmen learning calculus basics.

GeoGebra Commands & Parameters

  1. Numeric c(2)
  2. f(x) = c^(x)
  3. f'(x) = f'(x)
  4. Numeric a(-7)
  5. (a, f(a))
  6. (a, f'(a))
  7. f'(x)
  8. Boolean b(false)
  9. g(x) = If[a - 0.5 ≤ x ≤ a + 0.5, f(a) + (f'(a) * (x - a))]

AI Drawing Prompt Reference

Draw a graph of a function and its derivative. The function is an exponential function, and the derivative is a linear approximation. Key objects include the function graph, derivative graph, origin, function value, and derivative value. Construction order: first draw the function graph, then the derivative graph, and finally label key points.
The prompt above was compiled from the original drawing commands and is for reference only.