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When f'(x) = f(x)

When f'(x) = f(x)
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2016-09-27 09:12
FunctionDerivative
In collections BC Calculus
This example demonstrates that the only functions whose derivative is equal to themselves are exponential functions. Key concepts include derivatives and exponential functions. Constructed using GeoGebra commands such as Point, Circle, Tangent, etc., it is suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. Point(f) → A
  2. Circle(A, 2) → c
  3. Tangent(A, f) → h
  4. Intersect(c, h) → B, C
  5. Vector(A, C) → u
  6. Vector(A, B) → v
  7. Intersect(g, i, (-1.4469407665505223, -2.18592458124899)) → D
  8. Textfield(a) → InputBox1