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Exploring the Derivative of Exponential Functions by Mak Desmond

Exploring the Derivative of Exponential Functions by Mak Desmond
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2017-05-26 11:57
FunctionCalculusDerivative
This example demonstrates the relationship between exponential functions and their derivatives graphically. It involves core math concepts like derivatives, exponential functions, function graphs, ratios, and percentages. GeoGebra commands and objects used include Point, Tangent, Slope, Name, and LaTeX for construction. Suitable for high school calculus introduction and teaching.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Tangent(A, f) → b
  3. Slope(b) → m
  4. Name(m) → C1_1
  5. Name(m) → C1
  6. Name(a) → E1_1
  7. Name(a) → E1_2
  8. Name(a) → E1_3
  9. Name(a) → E1
  10. LaTeX(f, true, true) → text2

AI Drawing Prompt Reference

Draw an exponential function and its derivative. First, plot the exponential function. Then, select a point on the function and draw the tangent line at that point. Next, label the slope of the tangent line as the derivative value. Finally, display the equation of the exponential function using LaTeX below the graph.
The prompt above was compiled from the original drawing commands and is for reference only.