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y=x Integral and Derivative Demo

y=x Integral and Derivative Demo
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2020-11-06 01:30
FunctionCalculusDerivativeIntegralGraphing
This example demonstrates the geometric relationship between the graph of y=x, its integral area, and the derivative (tangent line). Core math concepts include function graph, integral, derivative, tangent line, and slope. GeoGebra commands used are Integral, Derivative, Intersect, OrthogonalLine, Point, Polygon, Line, Slope, and Tangent. Suitable for high school mathematics teaching to understand the properties of basic elementary functions in calculus.

GeoGebra Commands & Parameters

  1. Integral(a(x)) → f_3
  2. Derivative(a(x)) → a'
  3. Intersect(a, f_3, 1) → C
  4. OrthogonalLine(C, yAxis) → f
  5. Point(f) → A
  6. OrthogonalLine(A, f) → g
  7. Intersect(a', g, 1) → D
  8. Polygon(C, A, D) → t2, d, c_2, a_2
  9. OrthogonalLine(A, xAxis) → h
  10. Integral(a(x), 0, 1) → b
  11. Point(xAxis) → B
  12. Line(C, B) → i
  13. OrthogonalLine(B, i) → j
  14. Intersect(b, f_3, 2) → E
  15. Intersect(b, f_3, 2) → F
  16. Intersect(f_3, j, 1) → G
  17. Polygon(C, B, G) → t1, g_1, c, b_1
  18. Intersect(a, c_2, 1) → H
  19. Slope(c_2) → m
  20. Tangent(H, a) → k
  21. Slope(c_2) → m_1
  22. Slope(k) → m_2

AI Drawing Prompt Reference

Draw the graph of the function y=x, then draw its integral curve and derivative curve. Find the intersection point C of the integral curve and the graph of y=x at x=1, draw a vertical line f through C, and take point A on f. Draw a line g perpendicular to f through A, and find the intersection point D of g and the derivative curve a'. Use points C, A, and D to draw a quadrilateral. Find point B on the x-axis, draw a line i through C and B, and draw a line j perpendicular to B. Find points E and F where the integral curve b intersects f_3, and find the intersection point G of f_3 and j. Use points C, B, and G to draw a quadrilateral. Find point H on the graph of y=x, draw a tangent line k through H, and label the slope m_2 of line k, as well as the slope m_1 of the derivative curve a' at point H.
The prompt above was compiled from the original drawing commands and is for reference only.