Growing and Growing: Visualizing Growth Rate with Derivatives and Inequalities

This example demonstrates the idea of “growing and growing” by turning growth behavior into a visible geometric/graph-based model. It connects growth trends to key analytical concepts: functions (how quantities vary), the derivative (as the instantaneous rate of change), and inequalities that capture when one growth relationship dominates another. In the visualization, planar figures (e.g., polygonal shapes such as rhombus-like constructions) provide a structured geometric framework, while the mathematical relationships determine the evolving features (e.g., boundaries/regions or comparison outcomes). Since the provided GeoGebra construction summary is empty, the exact GeoGebra commands and intermediate objects cannot be extracted; nonetheless, the typical workflow is to define the underlying function or relationship, render the relevant curve/region, and apply inequality conditions to emphasize the growth stage. Suitable for upper-secondary students transitioning toward calculus concepts, and for classroom activities that link derivative meaning to growth-rate intuition.