When a Secant Becomes a Tangent
by Anonymous · ⭐ 0 · 🍴 0
Bring two points closer and watch the secant’s slope approach the tangent’s slope. Move it by hand from average rate of change to the derivative—and the derivative function.
About this app
An interactive high-school calculus app that demonstrates how a secant line approaches a tangent as two points on a curve move closer together. Explore average rate of change, the derivative at a point, and the derivative function using three selectable functions: x²/2, x³/6 − 2x, and 3 − x²/2. Guided missions and adjustable controls help learners connect slope, tangent lines, and f′(x).
Use cases
- High-school students learning differentiation
- Teachers demonstrating secants and tangents
- Self-study of average rate of change
- Practice identifying positive, negative, and zero slopes
Features
- Adjust the base point a and gap h for a secant line
- Watch the secant slope approach the tangent slope
- Explore tangent lines for three different functions
- Move the tangency point and observe f′(a)
- Compare a function f(x) with its derivative f′(x)
- Complete guided missions with feedback