Interactive Function Tangent Line Practice with Derivatives

This example demonstrates how to construct a tangent line to a function at a chosen point and then verify whether the proposed line is the correct tangent using derivative information and geometric conditions. The key math concepts are the derivative as the slope of the tangent line, local linear approximation at the point of tangency, and the tangent condition that the line matches the curve’s direction at the contact point. Construction focuses on GeoGebra commands and interactive objects: Tangent is used to create the tangent line element (e.g., L); Derivative provides the slope information; Textfield and InputBox objects collect user inputs such as the point (a) and check parameters; If supports conditional logic for automated checking (e.g., checkTangent / checkDeriv); Segment and related visual elements display the tangent segment and the relevant geometric setup. Suitable for high school to early college students learning derivatives and tangent line interpretation.