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📐 The Derivative as a Limit

Drag a secant line's second point closer to a fixed point on a 3D curve and watch it converge into the tangent line, visualizing the limit definition of the derivative.

Mathematics3DModerate60 FPS

A red secant line connects two points on a 3D curve; as the offset h shrinks toward zero, the secant's slope converges onto the blue tangent line's exact slope — the limit that defines the derivative.

🔬 What It Demonstrates

The difference quotient [f(a+h) − f(a)] / h is the slope of a secant line. As h → 0, that slope approaches f'(a), the slope of the tangent line — the formal limit definition of the derivative.

🎮 How to Use

Pick a function, set the fixed point a, then drag h down toward zero (or tick "Animate h → 0") and watch the secant slope and difference shrink toward the tangent slope.

💡 Did You Know?

Newton and Leibniz independently formalized this exact limiting process in the 17th century, and the notation dy/dx still literally means "an infinitesimally small h."

⚙ Under the hood

Interactive 3D curve where dragging a secant line's second point closer to a fixed point shows it converging into the tangent line, visualizing the limit definition of the derivative.

derivativelimitscalculustangent-linesecant-linemathematics

3D · Three.js / WebGL renderer · 60 FPS target · runs fully client-side, no install