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Derivatives and Tangents

Derivatives and Tangents
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2018-10-03 03:40
FunctionCalculusDerivative
This example demonstrates the concepts of derivatives and tangents. By finding the derivative f'(x) of a function f(x), we can determine the tangent line at a specific point. The construction uses commands such as If, Derivative, Point, Circle, Intersect, and Segment. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. If(Example ≟ 1, (-0.02 * x^(3)) + (0.2 * x^(2)) + (0.07 * x) + 3.06, Example ≟ 2, (0.002 * x^(4)) - (0.03 * x^(3)) + (0.13 * x^(2)) + (0.15 * x) + 3.56, Example ≟ 3, (2 * cos(x)) + 6) → f
  2. Derivative(f) → f'
  3. Point(g) → J
  4. Point(h) → K
  5. Point(i) → L
  6. Point(j) → M
  7. Point(l) → N
  8. Point(m) → O
  9. Point(n) → P
  10. Point(p) → Q
  11. Point(q) → R
  12. Circle(E, 1) → c
  13. Intersect(c, r) → S, T
  14. Segment(S, T) → s
  15. Circle(A, 1) → d
  16. Intersect(d, t) → U, V
  17. Segment(U, V) → e
  18. Circle(F, 1) → c_1
  19. Intersect(c_1, f_1) → W, Z
  20. Segment(W, Z) → g_1
  21. Circle(B, 1) → d_1
  22. Intersect(d_1, h_1) → A_1, B_1
  23. Segment(A_1, B_1) → i_1
  24. Circle(G, 1) → e_1
  25. Intersect(e_1, j_1) → C_1, D_1
  26. Segment(C_1, D_1) → k_1
  27. Circle(C, 1) → p_1
  28. Intersect(p_1, l_1) → E_1, F_1
  29. Segment(E_1, F_1) → m_1
  30. Circle(H, 1) → q_1
  31. Intersect(q_1, n_1) → G_1, H_1
  32. Segment(G_1, H_1) → r_1
  33. Circle(D, 1) → s_1
  34. Intersect(s_1, t_1) → I_1, J_1
  35. Segment(I_1, J_1) → a_1
  36. Circle(I, 1) → c_2
  37. Intersect(c_2, b_1) → K_1, L_1
  38. Segment(K_1, L_1) → f_2

AI Drawing Prompt Reference

Draw a function and its derivative curve, along with tangent lines at specific points. First, draw the function f(x) = -0.02x^3 + 0.2x^2 + 0.07x + 3.06, then calculate its derivative f'(x). Next, select several points on the function graph, such as J, K, L, M, N, O, P, Q, R, and draw circles with radius 1 centered at these points. Find the intersection points of these circles with the function graph and connect them with line segments. Finally, select points S, T, U, V, W, Z, A_1, B_1, C_1, D_1, E_1, F_1, G_1, H_1, I_1, J_1, K_1, L_1, M_1, N_1, O_1, P_1, Q_1, R_1, S_1, T_1, U_1, V_1, W_1, X_1, Y_1, Z_1, draw corresponding circles and line segments, forming a complex structure.
The prompt above was compiled from the original drawing commands and is for reference only.