ICME Function Loupe II: Visualizing Slope Functions

This interactive GeoGebra example demonstrates the concept of the derivative by using a 'loupe' (magnifying glass) to zoom into a function graph around a point, revealing the local slope and dynamically plotting the corresponding slope function. The core mathematical ideas include functions, secant lines, tangent lines, and the limit definition of the derivative. Users can input a custom function via a text field, drag point A, or adjust parameter h to see how the secant slope approaches the tangent slope. The construction employs commands such as Textfield, Point, Segment, Midpoint, Locus, Line, and Polygon to build the loupe interface and generate the slope function locus. This resource is ideal for high school or introductory college calculus courses, helping students grasp the geometric meaning of derivatives through hands-on exploration and visual feedback.