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Value Tables and Rate of Change Task

Value Tables and Rate of Change Task
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2017-07-14 03:21
FunctionCalculusDerivative
This example demonstrates the rate of change of a function through value tables. Key mathematical concepts include functions, derivatives, and rates of change. It uses GeoGebra commands like TableText and Textfield for construction. Suitable for high school math education to help students understand the instantaneous rate of change of functions.

GeoGebra Commands & Parameters

  1. TableText({{a, b}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}, {A6, B6}, {A7, B7}, {A8, B8}}, "|_r") → text1
  2. TableText({{a, b_1}, {A10, B10}, {A11, B11}, {A12, B12}, {A13, B13}, {A14, B14}, {A15, B15}, {A16, B16}}, "|_r") → text2
  3. TableText({{a, b_2}, {A18, B18}, {A19, B19}, {A20, B20}, {A21, B21}, {A22, B22}, {A23, B23}, {A24, B24}}, "|_r") → text3
  4. TableText({{a, b_3}, {D2, E2}, {D3, E3}, {D4, E4}, {D5, E5}, {D6, E6}, {D7, E7}, {D8, E8}, {D9, E9}}, "|_r") → text4
  5. TableText({{a, b_4}, {D11, E11}, {D12, E12}, {D13, E13}, {D14, E14}, {D15, E15}, {D16, E16}, {D17, E17}}, "|_r") → text5
  6. TableText({{a, b_5}, {D19, E19}, {D20, E20}, {D21, E21}, {D22, E22}, {D23, E23}, {D24, E24}, {D25, E25}}, "|_r") → text6
  7. Textfield(f_1) → InputBox1
  8. Textfield(f_3) → InputBox3
  9. Textfield(f_4) → InputBox4
  10. Textfield(f_6) → InputBox6
  11. Textfield(f_5) → InputBox5
  12. Textfield(f_2) → InputBox2

AI Drawing Prompt Reference

Draw a function and its derivative values at different points, showing the changes in function values and derivative values through tables. First, plot the function, then calculate and display the derivative values at specified points, and finally show these points' function values and derivative values in a table format.
The prompt above was compiled from the original drawing commands and is for reference only.