Differentiable function

A function f(x) is differentiable at the point a if and only if, as x approaches a (which it is never allowed to reach), the value of the quotient:

approaches a limiting value that we call the derivative of the function f(x) at x=a.

There is also the more rigorous definition: a function f is said to be differntiable at point a if ∀ ∃​ such that if

then

.