Derivatives and Tangent Slopes
by Anonymous
Slide two points together to watch the secant's slope approach the tangent's slope—the derivative at that point.
About this app
An interactive calculus visualizer that shows how a secant slope approaches the tangent slope, or derivative, as the gap h shrinks. Explore three sections—Secant, Tangent, and Derivative—with graphs for y = x²/2 and additional functions including x³/6 − 2x and 3 − x²/2. Step through guided missions by moving the base or tangent point and comparing curve slopes.
Use cases
- High school students learning the definition of a derivative
- Teachers demonstrating secant-to-tangent convergence
- Learners exploring positive, negative, and zero slopes
- Classroom practice with tangent lines and derivative graphs
Features
- Interactive secant graph with adjustable base point a and gap h
- Tangent-line visualization with three selectable functions
- Derivative graph shown alongside the original function
- Guided missions with reset and next controls
- Live slope values and feedback about curve direction