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Directional Derivatives Demo by Ku, Yin Bon (Albert)

Directional Derivatives Demo by Ku, Yin Bon (Albert)
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2015-10-06 01:20
VectorCalculusDerivative
This example demonstrates the geometric interpretation of directional derivatives, visually showing how the derivative concept changes with vector and tangent line angles. Core math concepts include derivatives, vectors, tangent slopes, and integrals. GeoGebra commands and objects used in construction are Textfield, Segment, Circle, Point, Vector, CurveCartesian, IntegralBetween, Tangent, Slope. Suitable for university calculus courses or math enthusiasts studying directional derivatives and their applications.

GeoGebra Commands & Parameters

  1. Textfield(f) → inputBox1
  2. Segment(P, A) → a
  3. Circle(A, 1) → c
  4. Point(c) → B
  5. Vector(A, B) → u
  6. CurveCartesian(x(A) + (t * x(u)), y(A) + (t * y(u)), f(x(A) + (t * x(u)), y(A) + (t * y(u))), t, -1, 1) → b
  7. Segment(D, B) → d
  8. Segment(E, D) → e
  9. IntegralBetween(f(x(A) + (x * x(u)), y(A) + (x * y(u))), 0, -1, 1) → h
  10. Tangent(0, g) → i
  11. Segment(C, B) → j
  12. Circle(A, B) → k
  13. Slope(i) → duf
  14. Segment(F, G) → l