H 3.4 Derivatives: Tangent, Slope, and Riemann Sums

① This GeoGebra example dynamically visualizes the tangent line, its slope, and upper/lower Riemann sums for a function f, illustrating the geometric connection between derivatives and integrals. ② Core mathematical concepts include derivatives (slope of tangent), indefinite integrals, exponential functions, inequalities, vectors, and Riemann sums (upper and lower sums), bridging differential and integral calculus. ③ Construction highlights: the Point command creates a movable point A, Tangent generates the tangent line t, Slope computes its slope m, Segment builds segments S for Riemann sum rectangles, and an auxiliary function g is defined; these objects form an interactive diagram. ④ Suitable for high school seniors or early college calculus students, ideal for classroom demonstrations or self-study to deepen understanding of derivative definitions, tangent slope approximation, and integral approximation.