Tangent Through Point Touching Function

This example demonstrates how to construct a tangent line to a function's graph through a given external point, dynamically showing the point of tangency and the tangent equation. Core mathematical concepts include the geometric meaning of the derivative (the tangent slope equals the derivative at the point), solving tangent line equations, and properties of functions such as hyperbolas and subtraction. Construction highlights: using GeoGebra's Tangent command with function f and point P, generating related equation eq1 and auxiliary objects g and g_1 to visually illustrate the tangency condition. Suitable for high school and early college students to understand the relationship between derivatives and tangents, and as an interactive demonstration for introductory calculus.