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Directional Derivatives Demo

Directional Derivatives Demo
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2020-02-12 23:06
VectorFunctionCalculusDerivativeGeometric Construction
This example demonstrates the geometric interpretation of directional derivatives by dynamically showing the rate of change of a function at a point along any direction using vectors. Key math concepts include derivatives, vectors, limits, and multivariable calculus. Construction involves commands like Textfield, Segment, Circle, Point, Vector, IntegralBetween, Tangent, Slope, CurveCartesian, Plane, with key objects such as A, f, P, a, u, B, C, D, d, E, e, h, g, i, F, j, k, duf, G, l, text1, b, p, m, n. Suitable for university-level mathematics, calculus courses, or self-study to understand directional derivatives calculation and application.

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. Segment(D, B) → d
  7. Segment(E, D) → e
  8. IntegralBetween(f(x(A) + (x * x(u)), y(A) + (x * y(u))), 0, -1, 1) → h
  9. Tangent(0, g) → i
  10. Segment(C, B) → j
  11. Circle(A, B) → k
  12. Slope(i) → duf
  13. Segment(F, G) → l
  14. CurveCartesian(x(A) + (t * x(u)), y(A) + (t * y(u)), f(x(A) + (t * x(u)), y(A) + (t * y(u))), t, -10, 10) → b
  15. Plane(A, B, P) → m

AI Drawing Prompt Reference

Draw the geometric interpretation of the directional derivative of function f at point P. Start by plotting function f, then draw a unit circle at point A and select any point B on the circle to form vector u from A to B. Next, draw a line from A in the direction of vector u and calculate the angle between this line and the tangent line of f at point A, which represents the directional derivative. Finally, draw a plane through points A, B, and P, and plot the graph of function f on this plane.
The prompt above was compiled from the original drawing commands and is for reference only.