Local Linearity
In calculus (a branch of mathematics), a differentiable function is a function whose derivative exists at each point in its domain. The graph of a differentiable function must have a non-vertical tangent line at each point in its domain. As a result, the graph of a differentiable function must be relatively smooth, and cannot contain any breaks, bends, cusps, or any points with a vertical tangent.
More generally, if x0 is a point in the domain of a function ƒ, then ƒ is said to be differentiable at x0 if the derivative ƒ′(x0) exists. This means that the graph of ƒ has a non-vertical tangent line at the point (x0, ƒ(x0)). The function ƒ may also be called locally linear at x0, as it can be well approximated by a linear function near this point.
Read more about Local Linearity: Differentiability and Continuity, Differentiability Classes, Differentiability in Higher Dimensions, Differentiability in Complex Analysis, Differentiable Functions On Manifolds
Famous quotes containing the word local:
“Resorts advertised for waitresses, specifying that they “must appear in short clothes or no engagement.” Below a Gospel Guide column headed, “Where our Local Divines Will Hang Out Tomorrow,” was an account of spirited gun play at the Bon Ton. In Jeff Winney’s California Concert Hall, patrons “bucked the tiger” under the watchful eye of Kitty Crawhurst, popular “lady” gambler.”
—Administration in the State of Colo, U.S. public relief program (1935-1943)