Tangent Planes and Linear Approximation
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This example demonstrates the tangent plane to a function at a point and its linear approximation in 3D space. Key math concepts include tangent plane equations, partial derivatives, vector operations, and linear approximation. It uses GeoGebra commands like Vector, objects f, a, b, A, partial derivatives f_{x}, f_{y}, vectors u, v, w, and the tangent plane T_{(a,b)}. Suitable for university calculus courses to visualize and understand these concepts.
GeoGebra Commands & Parameters
Vector(A, A + (1, 0, f_{x}(a, b))) → uVector(A, A + (0, 1, f_{y}(a, b))) → vVector(A, A + u ⊗ v) → w
AI Drawing Prompt Reference
Draw the tangent plane to a function at point (a, b) and its linear approximation. Start by drawing two vectors u and v from point A in the x and y directions, respectively. Then, construct a third vector w using u and v. Finally, use these vectors to create the tangent plane T_{(a,b)}.
The prompt above was compiled from the original drawing commands and is for reference only.