MathPlotAI Logo MathPlotAI

Derivative of a Polynomial Function

Derivative of a Polynomial Function
Loading the math board and drawing, please wait…
2020-11-04 02:18
FunctionCalculusDerivative
This example demonstrates the relationship between polynomial functions and their derivatives, including graph transformations, extremum points, and turning points. It involves core math concepts like derivatives and function graphs. Constructed using GeoGebra commands/objects such as Textfield, Root, Extremum, TurningPoint, LaTeX, and variables a_8 to a_0, along with multiple InputBoxes and text elements. Suitable for high school and above students learning basic calculus and polynomial function properties.

GeoGebra Commands & Parameters

  1. Textfield(a_3) → InputBox1
  2. Textfield(a_2) → InputBox2
  3. Textfield(a_1) → InputBox3
  4. Textfield(a_0) → InputBox4
  5. Textfield(a_4) → InputBox5
  6. Textfield(a_5) → InputBox6
  7. Textfield(a_6) → InputBox7
  8. Textfield(a_7) → InputBox8
  9. Textfield(a_8) → InputBox9
  10. Root(f) → A, B, C, E, J, K, L, M
  11. Root(f') → F, G, H, I, N, O, P
  12. Extremum(f) → Q, R, S, T, U, V, W
  13. TurningPoint(f) → Z, A_1, B_1, C_1, D_1, E_1
  14. Extremum(f') → F_1, G_1, H_1, I_1, J_1, K_1
  15. Textfield(xmin) → InputBox10
  16. Textfield(xmax) → InputBox11
  17. Textfield(ymin) → InputBox12
  18. Textfield(ymax) → InputBox13
  19. LaTeX(text6, true, true) → text5

AI Drawing Prompt Reference

Draw a polynomial function and its derivative, including roots, extremum points, and inflection points. Input coefficients a_8 to a_0, and adjust the x and y axis ranges. First input the coefficients, then plot the polynomial function f(x), and subsequently plot its derivative f'(x). Mark all roots, extremum points, and inflection points.
The prompt above was compiled from the original drawing commands and is for reference only.