Tangent Plane to a Surface by Kristen Beck

Tangent Plane to a Surface by Kristen Beck
Loading the math board and drawing, please wait…
2016-09-24 04:10
In collections Multivariable Calculus
This example demonstrates how to draw the tangent plane to a surface at a specific point in 3D space. It involves core mathematical concepts such as tangent planes, surfaces, vectors, derivatives, and analytical geometry. Key GeoGebra commands and objects used include PointIn (point on surface), Derivative (derivative calculation), Line (line construction), OrthogonalPlane (orthogonal plane), and Vector (vector operations). Suitable for high school and above students learning calculus and spatial geometry concepts related to tangent planes.

GeoGebra Commands & Parameters

  1. PointIn(f) → P
  2. Derivative(f, x) → f_x
  3. Derivative(f, y) → f_y
  4. Line(P, g) → L
  5. OrthogonalPlane(P, L) → a
  6. Line(P, Vector[(1, 0, Δx)]) → h
  7. Line(P, Vector[(0, 1, Δy)]) → i
  8. Vector(P, P + g) → u