Derivative Explorer

Move Q toward P and watch the secant line become the tangent line.

Function / interpretation Point P: Horizontal change h = Δx:

P =

Q =

Δx =

Δy =

Average rate / secant slope =

Instantaneous rate / derivative =

Ask students: "What happens to the secant slope as h approaches 0?"

Teaching sequence: first let students estimate the slope with a large h, then reduce h manually, then run the animation. Emphasize that the derivative is a limit of average rates.

function P and tangent Q and secant Δx / Δy