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Critical Points

Critical Points
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2016-12-09 12:48
FunctionCalculusDerivativeIntegralGeometric Construction
This example demonstrates how to find the critical points of a function. Critical points are where the first derivative of a function is zero or undefined. By constructing the derivative of the function, we can locate these points. The example uses commands such as IntegralBetween, Intersect, Point, Segment, Tangent, and OrthogonalLine, suitable for high school mathematics education.

GeoGebra Commands & Parameters

  1. IntegralBetween(g, f, 0, 2) → b
  2. Intersect(b, f, 1) → A
  3. Intersect(b, f, 1) → B
  4. Intersect(b, f, 1) → C
  5. IntegralBetween(f, p, -1.9, 0) → a
  6. Point(yAxis) → F
  7. Point(yAxis) → G
  8. Segment(D, E) → h
  9. Segment(F, G) → i
  10. Segment(H, I) → j
  11. Point(f) → J_1
  12. Tangent(J_1, f) → k
  13. OrthogonalLine(J_1, k) → l