Geometric Visualization of the Derivative of an Inverse Function

This GeoGebra example geometrically visualizes the reciprocal relationship between the derivatives of a function and its inverse at symmetric points across the line $y=x$. The core mathematical concepts covered include inverse functions, derivatives, tangent lines, slopes, and the inverse function theorem. To construct this visualization, the `Function` command is used to define the function $f$ and its inverse $g$, the `Point` command is applied to mark corresponding points $A$ and $B$, and the `Tangent` command generates the tangent lines at these key points to illustrate the slopes dynamically. Text labels are added to show the algebraic relations. This tool is highly suitable for calculus classrooms, university-level mathematics courses, or high school advanced placement classes to build geometric intuition for the derivative rule of inverse functions.