IntroDerivatives
Tangent Lines
Overview
The tangent line at a point has slope equal to f′(a). It locally approximates the curve and is foundational to linearization.
Key Concepts
1
Tangent line at x=a: y = f(a) + f′(a)(x − a)
2
Normal line is perpendicular: slope = −1/f′(a)
3
Visualizable by moving a point along the curve
See it in action
Use the interactive visualizer to explore this concept with real graphs.