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Exercise 4: Optimization Problems

Exercise 4: Optimization Problems
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2017-07-27 22:13
FunctionDerivativeOptimization
This example demonstrates solving optimization problems to find the maximum and minimum values of a function. Key mathematical concepts include functions, derivatives, and extrema. Using GeoGebra commands such as Random, Line, and Textfield, parameters can be dynamically adjusted to observe changes in the function graph. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Random(-10, 10) → n_1
  2. Line(B, A) → a
  3. Textfield(deltay) → InputBox2
  4. Random(-5, 5) → m
  5. Random(-10, 10) → n
  6. Textfield(b) → InputBox3
  7. Random(1, 10) → deltax_1
  8. Sequence(((deltax_1 * i), b + (deltay * i)), i, -20, 20) → list1
  9. Sequence(Segment[A + ((deltax_1 * (i + 1)), (deltay * i)), A + ((deltax_1 * (i + 1)), (deltay * (i + 1)))], i, -20, 20) → rises
  10. Sequence(Segment[A + ((deltax_1 * i), (deltay * i)), A + ((deltax_1 * (i + 1)), (deltay * i))], i, -20, 20) → runs
  11. TableText({{p, k, l}, {A7, B7, C7}, {A8, B8, C8}, {A9, B9, C9}, {A10, B10, C10}, {A11, B11, C11}, {A12, B12, C12}, {A13, B13, C13}, {A14, B14, C14}, {A15, B15, C15}, {A16, B16, C16}}, "|_r") → text2