Directional Derivatives Demo by Laura del Río
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intersection: surface-surface, curve-curve
This example demonstrates the geometric interpretation of directional derivatives by moving a point on the function graph and displaying the tangent line, visually illustrating the concept of directional derivatives. Key mathematical concepts include directional derivatives, gradients, vectors, and tangent line equations. Construction highlights involve using commands like Derivative, Circle, Point, Vector, Translate, Textfield, Segment, CurveCartesian, and Line. Suitable for high school and above students studying calculus to understand the calculation and application of directional derivatives.
GeoGebra Commands & Parameters
Derivative(f, x) → DfDerivative(f, y) → Df_yCircle(P_{0}, 1) → c_1Point(c_1) → AVector(P_{0}, A) → u_1Translate(Q, v) → Q'Vector(Q, Q') → u_2Textfield(f) → CasillaDeEntrada1Segment(P_{0}, Q) → a_1CurveCartesian((x(u_1) * T) + x(P_{0}), (y(u_1) * T) + y(P_{0}), f((x(u_1) * T) + x(P_{0}), (y(u_1) * T) + y(P_{0})), T, x(P_{0}) - 10, x(P_{0}) + 10) → bTranslate(Q, v) → Q'_2Vector(Q, Q'_2) → eLine(Q, e) → d_1Vector(P_{0}, A) → u