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:
“Hey, you dress up our town very nicely. You don’t look out the Chamber of Commerce is going to list you in their publicity with the local attractions.”
—Robert M. Fresco, and Jack Arnold. Dr. Matt Hastings (John Agar)