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Partial Derivatives and Tangent Plane of a Function

Partial Derivatives and Tangent Plane of a Function
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2019-03-06 23:10
Coordinate GeometryCalculusDerivative
This example illustrates the partial derivatives and the corresponding tangent plane of a function at a point. Key mathematical concepts include partial derivatives and tangent planes. Using GeoGebra commands such as IntersectPath, Derivative, and Line, the example provides a visual understanding of these concepts. Suitable for university-level calculus courses.

GeoGebra Commands & Parameters

  1. IntersectPath(c, a) → d
  2. IntersectPath(b, a) → e
  3. Derivative(a, x) → g
  4. Derivative(a, y) → h
  5. Line(T, Vector[(1, 0, g(x_{0}, y_{0}))]) → i
  6. Line(T, Vector[(0, 1, h(x_{0}, y_{0}))]) → f
  7. Vector((1, 0, g(x_{0}, y_{0}))) → t_{x}
  8. Vector((0, 1, h(x_{0}, y_{0}))) → t_{y}
  9. Vector(T, T + (5 * t_{x}) ⊗ t_{y}) → n
  10. Vector(T, T + (5 * t_{x})) → u
  11. Vector(T, T + (5 * t_{y})) → v
  12. Segment(T, T_{0}) → j
  13. Surface(x_{0} + u, y_{0} + v, a(x_{0}, y_{0}) + (u * g(x_{0}, y_{0})) + (v * h(x_{0}, y_{0})), u, -3, 3, v, -3, 3) → k

AI Drawing Prompt Reference

Draw the function surface and its tangent plane at a point. First, plot the function surface. Then, calculate the partial derivatives at the point. Next, draw the tangent lines at the point. Finally, construct the tangent plane using the partial derivatives.
The prompt above was compiled from the original drawing commands and is for reference only.