Graphical Construction of Derivatives and Tangent Slopes

This example demonstrates the geometric meaning of derivatives by drawing the tangent line on a function graph and visualizing its slope as a local rate of change. It centers on core ideas from Calculus: the derivative, the tangent slope (Slope), representing the function and its derivative (f and f'), and using these to interpret how the graph changes at a chosen point. In the GeoGebra construction, Derivative is used to compute/create the derivative object, Slope is used to obtain the tangent slope value, and Segment together with curve/point elements builds the tangent-line geometry. Textfield/Text objects provide labels such as f, f', and the slope-related variable. Interactive controls (buttons and input fields) update the selected point and refresh the tangent and slope display. Suitable for late high school and early college students learning or reviewing derivatives, tangent lines, and graphical understanding of local linear approximation.