# Differentiable function

### From Conservapedia

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 ε − δ definition: a function f is said to be differntiable at point *a* if ∀ε > 0 ∃δ > 0 such that if

then

- .