Triangle Area and Hyperbola-Cube Optimization Problem (ICPPF 3.0)

This example demonstrates a dynamic optimization problem combining triangles, hyperbolas, and cubes, exploring extrema of area or volume through an interactive GeoGebra interface. Core mathematical concepts include triangle area calculation, hyperbola equations, cube geometry, and optimization principles. Construction highlights: using commands such as Point, Vector, Textfield, and Sequence to create points, vectors, text boxes, and sequences; defining objects like a, b, X, f_2, g_2, B, C, f, g, c; using input boxes (inputBox1, inputBox2) to dynamically adjust parameters; generating multiple auxiliary points (A1 to A12) and segments to build an interactive optimization model. Suitable for high school or university students studying analytic geometry, functions, and optimization, as well as for teachers demonstrating dynamic mathematical modeling in class.