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Exploring Cubic Gradients

Exploring Cubic Gradients
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2016-09-14 17:36
FunctionCalculusDerivativeGraphing
This example demonstrates the relationship between cubic functions and their derivatives, involving core math concepts like derivatives, function graphs, and rates of change. It is constructed using GeoGebra commands such as If, panelleft1, panelleft2, Textfield, Sequence, Derivative, with objects like a, f_3, b, f_2, c, f_1, etc. Suitable for high school and above students to understand the geometric meaning of derivatives in calculus and properties of cubic functions.

GeoGebra Commands & Parameters

  1. If(a ≟ 1, x^(3), (a * x^(3))) → f_3
  2. If(b ≟ 1, x^(2), (b * x^(2))) → f_2
  3. If(c ≟ 1, x, (c * x)) → f_1
  4. panelleft1(240) → panel1, e, i, j, k, l
  5. panelleft2(240) → panel2, m, n, p, q, r
  6. Textfield(a) → InputBox1
  7. Textfield(b) → InputBox2
  8. Textfield(c) → InputBox3
  9. Sequence((i, f(i)), i, -4, 4) → intpoints
  10. If(b ≟ 0, If[c ≟ 0, f_3(x) + d, f_3(x) + f_1(x) + d], If[c ≟ 0, f_3(x) + f_2(x) + d, f_3(x) + f_2(x) + f_1(x) + d]) → g
  11. Textfield(d) → InputBox5
  12. Sequence(Segment[Intersect[Circle[(i, f(i)), 0.5], Line[(i, f(i)), (i + 1, f(i) + f'(i))], 1], Intersect[Circle[(i, f(i)), 0.5], Line[(i, f(i)), (i + 1, f(i) + f'(i))], 2]], i, -4, 4) → chords
  13. Sequence((i, f'(i)), i, -4, 4) → gradients
  14. Derivative(f) → f'