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Increasing and Decreasing Intervals of Functions

Increasing and Decreasing Intervals of Functions
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2015-12-03 05:17
FunctionCalculusDerivative
This GeoGebra applet illustrates the increasing and decreasing intervals of a function. Key mathematical concepts include derivatives and monotonicity of functions. By constructing the tangent, unit vector, and intervals, students can visually understand the increasing or decreasing nature of the function in different intervals. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Intersect(f', xAxis) → M, N
  2. Function(f, -4, 6.5) → g
  3. If((a > 0) ∧ (a < 1), X_1, If[(b ≥ 0) ∧ (b < 1) ∧ a ≟ 1, X_2, If[(c ≥ 0) ∧ (c < 1) ∧ b ≟ 1, X_3]]) → X
  4. Tangent(C, g) → e
  5. UnitVector(e) → u
  6. Segment(X, C) → d
  7. Segment(C - u, C + u) → h
  8. Segment(M, (x(M), g(x(M)))) → k
  9. Segment(N, (x(N), g(x(N)))) → l