Graphs of Derivatives: Visualizing Tangent Slopes

This GeoGebra example dynamically illustrates the relationship between a function f and its derivative f', making the geometric meaning of the derivative as the slope of the tangent line visually explicit. Core mathematical concepts include the definition of the derivative, tangent slope, and the correspondence between the sign of the derivative and the monotonicity of the function. Construction highlights: the Intersect command finds intersection points between the function and tangent lines, Tangent constructs the tangent line through a movable point P, Slope computes the slope value m, and Textfield creates input boxes to dynamically alter the function expression or parameters. Key objects include the function f, the moving point P, the tangent line d, the slope value m, and the traced graph of f'. This is suitable for high school calculus introduction or college-level elementary calculus, helping students grasp how the derivative graph relates to the original function and how to identify extrema through changes in tangent slope.