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Gradient and Directional Derivative

Gradient and Directional Derivative
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2020-02-13 15:38
VectorFunctionCalculusDerivativeGraphing
This example illustrates the concepts of gradient and directional derivative. By using the gradient vector of a function, we can understand the rate of change of the function in any direction at a given point. The construction involves commands like Point, Derivative, Vector, suitable for high school and above students learning calculus.

GeoGebra Commands & Parameters

  1. Point(g) → A
  2. Derivative(f, x) → f_x
  3. Derivative(f, y) → f_y
  4. Vector(A, A + (f_x(a, b), f_y(a, b))) → gradient
  5. Sequence(f(x, y) - k = 0, k, -4, 4, 0.5) → list1
  6. SolveODE(f_y(x, y), f_x(x, y), a, b, 4, 0.1) → numericalIntegral1
  7. Vector(B, C) → u
  8. Vector(B, D) → v
  9. Vector(B, E) → w
  10. Vector(B, F) → d