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Directional Derivative Geometric Exploration

Directional Derivative Geometric Exploration
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2019-01-01 02:49
VectorFunctionCoordinate GeometryCalculusDerivative
This GeoGebra applet explores the geometric significance of the directional derivative for a function of two variables. It visualizes how the derivative extends to arbitrary directions via tangent planes and direction vectors. Core concepts include partial derivatives, direction vectors, tangent planes, and surface geometry. Construction uses GeoGebra commands such as Circle, Point, Vector, Plane, Line, Segment, and CurveCartesian. Suitable for high school advanced mathematics or university calculus courses.

GeoGebra Commands & Parameters

  1. Circle(A, 1) → c
  2. Point(c) → B
  3. Vector(A, B) → u
  4. Vector(A, A + (h * u)) → v
  5. Plane(A, B, C) → a
  6. Line(C, E) → b
  7. Segment(C, A) → d
  8. Line(A, B) → g
  9. CurveCartesian(x(A) + (x(u) * t), y(A) + (y(u) * t), f(x(A) + (x(u) * t), y(A) + (y(u) * t)), t, -10, 10) → e