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Function Derivative & Hypothesis Testing Demo

Function Derivative & Hypothesis Testing Demo
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2018-08-07 02:30
FunctionCalculusDerivativeProbability & StatisticsGeometric Construction
This example demonstrates the geometric meaning of function derivatives and the process of hypothesis testing. It involves core math concepts like derivatives, natural logarithms, mean calculation, and hypothesis testing. Construction highlights include using GeoGebra commands such as Point, Vector, Textfield, Segment to create function graphs, tangents, data points, and statistical plots. Suitable for high school and above students learning the application of calculus and statistics.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. Vector(A, B) → u
  3. Textfield(f) → inputBox1
  4. Point(yAxis) → x_1
  5. Vector(x_1, y_1) → v
  6. Segment(f_x, F) → c
  7. Segment(E, F) → d
  8. Segment(A, x_1) → e
  9. Segment(B, y_1) → g
  10. Segment(B, y_1) → h

AI Drawing Prompt Reference

Draw a function graph and show the geometric meaning of its derivative. Start by plotting the coordinate axes, then mark a point on the x-axis and draw a vector from it to the function graph. Input a function expression and mark a point on the function graph, drawing a vector from it to the x-axis. Sketch the tangent line to the function graph and label the point of tangency. Finally, add some data points in the coordinate system and connect them with line segments to display a statistical plot.
The prompt above was compiled from the original drawing commands and is for reference only.