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Tangent Plane to Surface with Partial/Directional Derivatives

Tangent Plane to Surface with Partial/Directional Derivatives
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2017-06-29 02:36
FunctionCoordinate GeometrySolid GeometryCalculusDerivative
This example demonstrates how to construct the tangent plane to a surface using partial and directional derivatives. Key mathematical concepts include partial derivatives, directional derivatives, and tangent planes. It utilizes commands such as CurveCartesian, objects a, A, TanPlane, i, j, u_{1}, u_{θ}. Suitable for university-level calculus and coordinate geometry courses.

GeoGebra Commands & Parameters

  1. CurveCartesian(2 + t, 1 + (0 * t), 13 + (12 * t), t, -10, 10) → i
  2. CurveCartesian(2, 1 + t, 13 - t, t, -10, 10) → j
  3. CurveCartesian(2 + t / sqrt(5), 1 + ((2 * t)) / sqrt(5), 13 + ((2 * t) * sqrt(5)), t, -10, 10) → u_{1}
  4. CurveCartesian(2 + t / 2, 1 + (t * sqrt(3) / 2), 13 + (t * (6 - sqrt(3) / 2)), t, -10, 10) → u_{θ}