Directional Derivatives Demo by wuguoning

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2020-02-13 15:05

This example demonstrates the geometric interpretation of directional derivatives, showing how the rate of change of a function at a point varies along a specific direction using the angle between a vector and the tangent line. Key math concepts include derivatives, vectors, tangents, and geometric intuition. Construction involves commands like Textfield, Segment, Circle, Point, Vector, CurveCartesian, IntegralBetween, Tangent, Slope to visualize function graphs, tangent lines, and directional vectors. Suitable for university calculus courses or learners exploring intuitive directional derivative understanding.

GeoGebra Commands & Parameters

Textfield(f) → inputBox1
Segment(P, A) → a
Circle(A, 1) → c
Point(c) → B
Vector(A, B) → u
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
Segment(D, B) → d
Segment(E, D) → e
IntegralBetween(f(x(A) + (x * x(u)), y(A) + (x * y(u))), 0, -1, 1) → h
Tangent(0, g) → i
Segment(C, B) → j
Circle(A, B) → k
Slope(i) → duf
Segment(F, G) → l

AI Drawing Prompt Reference

Draw a 3D surface representing a function of two variables. Mark a base point on the surface. From this point, draw a unit circle in the domain and choose a direction vector ending on the circle. Construct a curve on the surface that follows this direction, with height given by the function values. At the base point, draw the tangent line to this curve and display its slope, which represents the directional derivative. Also connect the base point, the direction vector endpoint, and relevant points on the tangent line with segments. Include a text input field to dynamically change the function expression for exploring different directional derivatives.

The prompt above was compiled from the original drawing commands and is for reference only.