Calculus in motion.

One curve stays quiet while the thing that approximates or measures it moves. A chasing tangent, Riemann sums, area under a curve, a Taylor approximation and a slope field, ready to drop into a calculus explainer.

Chasing tangentA tangent line sliding the length of a cubic, slope in hand.
Riemann sumsMidpoint rectangles multiplying toward the smooth area.
Area under a curveThe upper limit sweeping, the filled region following it.
Taylor approximationA polynomial growing degree by degree onto cos(x).
Slope fieldy' = x - y, with one solution rethreading itself as it starts higher or lower.