MathPlotAI Logo MathPlotAI

Calculus Big Picture: Slope and Area Connection by Ken Schwartz

Calculus Big Picture: Slope and Area Connection by Ken Schwartz
Loading the math board and drawing, please wait…
2015-03-30 05:18
CalculusDerivativeIntegral
In collections AP Calculus AB Applet Collection
This example dynamically demonstrates the relationship between slope and area, visually illustrating core calculus concepts like derivatives, integrals, and limits. It uses commands such as Polygon, Segment, Integral, and Vector. Ideal for high school and university preparatory students studying calculus.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D, E) → poly1, a, b, c, d, e
  2. Segment(E, (t, p(t))) → pseg
  3. Tangent(Ppt, p) → tline
  4. Circle(Ppt, 1) → Pcir
  5. Intersect(Pcir, tline) → CP1, CP2
  6. Segment(CP1, CP2) → mseg
  7. Integral(v, 0, t) → Avel
  8. Segment((x(E), v(t)), (t, v(t))) → Vseg
  9. Vector((x(C), (0.5 * (y(A) + y(B)))), (x(C), (0.5 * (y(A) + y(B))) + (0.4 * sgn(v(t))))) → Vvec
  10. Segment((t, -2), (t, p(t))) → ptseg
  11. Segment((t, -2), (t, v(t))) → vtseg
  12. Vector((-0.45, v(t) + 0.6 - (0.2 * sgn(acc(t)))), (-0.45, v(t) + 0.6 + (0.2 * sgn(acc(t))))) → Cvec