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导数的定义及其几何意义

导数的定义及其几何意义
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2017-11-21 05:25
微积分导数几何作图
本范例演示了导数的定义及其几何意义，通过动态演示切线的概念和斜率的变化。涉及的核心数学概念包括导数、切线、斜率和极限。作图要点使用了GeoGebra的Point、Segment、Line、OrthogonalLine、Intersect、Angle、Tangent、If、LaTeX等命令和对象。适合高中及以上学生学习和理解微积分基础概念。

GeoGebra 命令及参数

  1. Point(f) → A
  2. Segment(A, C) → a
  3. Segment(B, B_1) → b
  4. Segment(D, A) → c
  5. Segment(E, B) → d
  6. Line(A, B) → r
  7. OrthogonalLine(A, b) → g
  8. Intersect(g, b) → F
  9. Segment(A, F) → i
  10. Line(E, B) → j
  11. Angle(g, r) → α
  12. Segment(B, F) → k
  13. Tangent(A, f) → e
  14. If(h ≠ 0, Angle[xAxis, r], Angle[xAxis, e]) → β
  15. LaTeX("\text{A function is } \textcolor{#FF0000}{\text{differentiable }} \text{at a point } x_0 \cr \text{if the } \textcolor{#0000FF}{\text{limit of the difference quotient exists}} \cr \text{as x approaches } x_0.") → testo4
  16. LaTeX("\textcolor{#FF0000}{\text{Geometrically}} \cr \text{ }\cr \text{The derivative of a function at a point } x_0 \cr \text{is the } \textcolor{#0000FF}{\text{slope of the tangent line }}\cr \text{to the graph of the function at }x_0.") → testo5