Derivative of a One-Variable Function

This GeoGebra example dynamically illustrates the derivative of a single-variable function, showing the slope of the tangent line at a movable point on the graph. Core mathematical concepts include the definition of the derivative, tangent line slope, continuity, and basic differential equation ideas. Construction uses the NDerivative command to compute the numerical derivative, Vector and Line commands to create the tangent vector and line, and a slider (a) to control the point of tangency, updating the derivative function graph in real time. Objects include function f, derivative function derivf, point A, points B, C, D, and text labels. Suitable for high school and early college students learning calculus, this example provides an intuitive visualization of how the derivative represents the rate of change of a function.