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Tangent to a Cubic Curve

Tangent to a Cubic Curve
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2017-03-04 21:11
FunctionCalculusDerivative
This example demonstrates the tangent to a cubic curve. Core mathematical concepts include derivatives and functions. Using GeoGebra commands such as If, panelleft1, panelleft2, Textfield, Sequence, Derivative, etc., the construction of a cubic curve and its tangent can be achieved. Suitable for high school mathematics education and learning.

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'

AI Drawing Prompt Reference

Draw a cubic curve and its tangent lines. First, input the coefficient a for the cubic term, then input the coefficients b and c for the quadratic and linear terms, and finally input the constant term d. Based on the input coefficients, draw the cubic curve f(x) = a*x^3 + b*x^2 + c*x + d. Then, calculate and draw the tangent lines at each integer point on the curve. Finally, display the derivative values at each integer point on the curve.
The prompt above was compiled from the original drawing commands and is for reference only.