Linear approximation
= Linear approximation
{title2=$f(a+h)=f(a)+f'(a)h+o(h)$}
{wiki}
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> $f(a)+f'(a)(x-a)$. The <chain rule> combines such local approximations through <function composition>; it does not assert their equality to the original <functions> over a finite <interval>.