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Equations of Tangents with Given Slope

Equations of Tangents with Given Slope
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2016-01-15 03:16
FunctionCalculusDerivative
This example demonstrates how to find the equations of tangents to a curve given a specific slope. Key mathematical concepts include derivatives and tangent lines. Using GeoGebra commands such as Derivative, Tangent, and Slope, dynamic constructions of tangents and their variations are explored. Suitable for high school calculus education.

GeoGebra Commands & Parameters

  1. Derivative(f) → f'
  2. Textfield(a) → InputBox1
  3. Point(list1) → A
  4. OrthogonalLine(A, xAxis) → b
  5. Point(list1) → B
  6. OrthogonalLine(B, xAxis) → c
  7. Intersect(f, b) → C
  8. Intersect(f, c) → D
  9. Tangent(C, f) → d
  10. Tangent(D, f) → e
  11. Slope(d) → m
  12. Slope(e) → m_1
  13. RotateText(text4, 80°) → text5

AI Drawing Prompt Reference

Draw a function curve and input a slope value to find the tangents to the curve with that slope. First, calculate the derivative of the curve, then construct two lines perpendicular to the x-axis using the input slope value, which intersect the curve at two points. Draw the tangents at these points and show the slopes of these tangents.
The prompt above was compiled from the original drawing commands and is for reference only.