Differentiable function
In calculus (a branch of mathematics), a
differentiable function of one real variable is a function whose derivative exists at each point in its domain. As a result, the graph of a differentiable function must have a non-vertical tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps. More generally, if
x0 is a point in the domain of a function
f, then
f is said to be
differentiable at x0 if the derivative
f′(
x0) exists. This means that the graph of
f has a non-vertical tangent line at the point (
x0,
f(
x0)). The function
f may also be called
locally linear at
x0, as it can be well approximated by a linear function near this point.