Assertion: function | /r/HasProperty | differentiable
Facets:
value: in the interval
type: TEMPORAL
value: at every point of the domain
type: LOCATION
value: everywhere
type: OTHER
value: continuously
type: TEMPORAL
value: in this section
type: OTHER
value: until the 19th century
type: TEMPORAL
Source sentences:
text: Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity).
text: The class C1 consists of all differentiable functions whose derivative is continuous; such functions are called continuously differentiable.
text: In this section, all functions are differentiable in some interval.
text: If the function is differentiable in the interval, it is monotonic if the sign of the derivative is constant in the interval.
text: At the very minimum, a function could be considered "smooth" if it is differentiable everywhere (hence continuous).
text: For many commonly used real functions, the domain is the whole set of real numbers, and the function is continuous and differentiable at every point of the domain.