 Linear approximation

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 $f(a)+f^{\prime }(a)(x-a)$. The chain rule combines such local approximations through function composition; it does not assert their equality to the original functions over a finite interval.

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.