Which One Changes Faster? Comparing Instantaneous Rates with Derivatives

This GeoGebra lesson demonstrates how to decide which of two functions (or curves) changes faster by comparing their instantaneous rates of change at a chosen point. The key math ideas are differential calculus: derivatives as local slopes, instantaneous speed/rate, and using tangent-line slope comparisons on function graphs. For construction, the source provided no GeoGebra construction summary (no specific commands or objects were listed), but the standard approach in GeoGebra is to plot the relevant functions, draw tangent lines at the same input value, and use the tangent slopes (derivative values) to determine which function changes faster; optional dynamic labels can display the computed rates. Suitable for upper-secondary through introductory university students, especially for teaching and learning derivatives, rate interpretation, and graphical reasoning. Also compatible with broader contexts that may connect to integral calculus and applied probability/statistics backgrounds, as suggested by the original topic tags.