Interactive Visualization of Increasing and Decreasing Functions

This GeoGebra applet provides an interactive visual demonstration of the increasing and decreasing intervals of a continuous function, helping students connect the algebraic sign of the derivative with the geometric behavior of the function graph. The core mathematical concepts include function monotonicity, first derivative test, tangent lines, and critical points. In terms of construction, the applet utilizes the Function command to plot the function f(x) and its derivative f'(x), while the If command is employed to dynamically color-code or highlight intervals based on the sign of the derivative. The Tangent command is used to draw local tangent lines at movable points, and UnitVector along with Segment are used to construct directional indicators showing the trend of increase or decrease. Intersection points are calculated using the Intersect command to mark local extrema. Interactive elements like buttons and custom variables manage the state of the demonstration. This tool is highly suitable for high school calculus introductory courses, college-level calculus classrooms, or self-paced online learning environments to illustrate the applications of derivatives.