Interactive resource
Derivative and Tangent Line Visualizer
Functions. See how a tangent line moves along a curve to build intuition for derivatives and instantaneous rate of change. Free interactive GeoGebra…
Overview
A derivative is an instantaneous rate; geometrically it is the tangent slope. Move the point of tangency and watch the line rotate.
Explanation
f'(x₀) is the slope of the tangent at x₀.
Definition: limit of secant slopes as Δx → 0.
Smaller Δx → secant hugs the tangent → slope nearer the derivative.
How to use
- Open the derivative–tangent scene.
- Move the point of tangency along the curve.
- Watch the tangent slope change.
- Connect the picture to the definition of the derivative.
Teaching tip
Slow down near extrema: the tangent flattens and the slope approaches 0.
Knowledge points
FAQ
Do students need differentiation rules first?
Use this as geometric motivation; practice algebraic rules afterward.
Is this tool free?
Yes. It runs in the browser with no install.
Good for class demos?
Yes — project it and ask what changes when you drag a parameter.
How do I write the formula afterward?
Open the equation editor or symbol sheet and copy a clean expression.