Directional Derivative Demo

Directional Derivative Demo
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2019-11-03 19:07
This example demonstrates the geometric interpretation of directional derivatives, visually showing the dot product between a vector and the gradient of a function. Key math concepts include directional derivatives, gradients, vector dot products, function graphs, and tangent lines. Constructed using commands like Circle, Vector, Textfield, Derivative, Segment, CurveCartesian, and Tangent to plot function graphs, gradient vectors, tangent lines, and directional derivative vectors. Suitable for high school students and above learning calculus and applications of directional derivatives.

GeoGebra Commands & Parameters

  1. Circle(A, 2) → c
  2. Vector(A, (x(A) + (2 * cos(alph)), y(A) + (2 * sin(alph)))) → u
  3. Textfield(f) → InputBox1
  4. Textfield(M) → InputBox2
  5. Derivative(f(x, y(M))) → fdx
  6. Derivative(f(x(M), x)) → fdy
  7. Vector(A, (x(A) + fdx(x(M)), y(A) + fdy(y(M)))) → v
  8. Segment((-1, 0), (9, 0)) → tmp1
  9. Segment((4, -1), (4, 8)) → h
  10. CurveCartesian(t + 4, f(x(M) + (t * cos(alph)), y(M) + (t * sin(alph))), t, -5, 5) → a
  11. Tangent(a(0), a) → i