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Mean Value Theorem Demonstration by M Braddock

Mean Value Theorem Demonstration by M Braddock
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2014-11-14 04:15
FunctionCalculusDerivativeGeometric ConstructionGraphing
This example dynamically illustrates the Mean Value Theorem, showing the geometric interpretation that a continuous function on a closed interval has a tangent parallel to the secant line connecting two points. Core math concepts include derivatives, continuous functions, and average value over an interval. Constructed using GeoGebra commands like a, b, g, f, A, B, s, c, C, t, s1, s2, h, p, text elements, suitable for high school and above learners exploring function properties and theorem applications.

GeoGebra Commands & Parameters

  1. Numeric a(-1)
  2. Numeric b(2)
  3. g(x) = (2 / 3 * x^(3)) - x^(2) + 1
  4. f(x) = If[a ≤ x ≤ b,g(x)]
  5. (a, f(a))
  6. (b, f(b))
  7. s(x) = ((f(b) - f(a)) / (b - a) * (x - a)) + f(a)
  8. Numeric c(0.23333321000000007)
  9. (c, f(c))
  10. t(x) = (f'(c) * (x - c)) + f(c)
  11. (f(b) - f(a)) / (b - a)
  12. f'(c)
  13. h(x) = If[c - 1.5 ≤ x ≤ c + 1.5,t]
  14. p(x) = If[a - 0.5 ≤ x ≤ b + 0.5,s]