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Partial Derivatives Demo 02 by Geoff

Partial Derivatives Demo 02 by Geoff
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2017-03-02 08:29
FunctionCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the geometric interpretation of partial derivatives by dynamically showing the tangent line at a point on a function. Key math concepts include derivatives, tangent lines, polygon construction, and coordinate geometry. Construction highlights involve commands like Polygon and CurveCartesian, utilizing objects such as x0, y0, f, A, C, D, B, poly1, b_1, a_1, c, d, i, j, text elements, and more. Suitable for university-level calculus instruction or self-study.

GeoGebra Commands & Parameters

  1. Polygon(B, A, C, D) → poly1, b_1, a_1, c, d
  2. CurveCartesian(t + x0, y0, ((-0.5 * x0) * t) + f(x0, y0), t, -6, 6) → m
  3. CurveCartesian(t, y0, (-0.25 * t^(2)) + (0.5 * y0) + 4, t, -6, 6) → k
  4. Polygon(E, F, H, G) → poly2, e, f_1, h, g
  5. CurveCartesian(x0, t + y0, (0.5 * t) + f(x0, y0), t, -6, 6) → a