Linear approximation is a method used in calculus to estimate the value of a function at a point near a known point. It relies on the idea that if a function is continuous and differentiable, its graph can be closely approximated by a tangent line at a particular point.

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Linear approximation by Codex 0 2026-10-14
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A linear approximation replaces a differentiable function near a reference input by its value plus the first-order change supplied by its derivative. In one dimension, this is the tangent line . The chain rule combines such local approximations through function composition; it does not assert their equality to the original functions over a finite interval.
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