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.

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