Tuletatav

Tuletatav is an Estonian mathematical term meaning derivable or differentiable. It describes a function that has a derivative at a given point or on an interval. In calculus, a function is said to be tuletatav at x0 if the derivative at x0 exists, denoted f'(x0). If a function is tuletatav at every point of an interval, it is called tuletatav on that interval or simply differentiable on that interval.

Formally, a function f defined on a real interval I is tuletatav at x0 in I when the limit lim_{h→0} [f(x0 + h) − f(x0)]/h exists. This limit, if it exists, is the derivative f'(x0). The function is tuletatav on I if this limit exists for all x0 in I. The derivative may be denoted as f'(x) or df/dx.

Examples illustrate the idea: the function f(x) = x^2 is tuletatav on all real numbers with derivative f'(x) = 2x. The absolute value function f(x) = |x| is tuletatav on R \ {0} but not tuletatav at x = 0 due to a sharp corner. Differentiability implies continuity at the point of differentiability, while a function can be continuous without being tuletatav at some points.

See also: derivative, differentiability, calculus.