This condition can be written in terms of epsilons and deltas as well. We say that f is differentiable at x0 if for any ε > 0 there exists a &delta > 0 such that
[f(x_0 + h) - f(x_0) - f'(x_0)h]/h < ε
[ f '(x0 - ε) h < f(x0 + h) - f(x0) < (f '(x0) + ε) h
whenever |h| < &delta. This definition is similar in form to the definition of continuity. Recall that in the geometrical interpretation of continuity the challenge was to find a small enough &delta-disc domain of x0 such that the graph of the function over the domain would lie between two horizontal bars a distance ε above and below f(x0). In the geometrical interpretation of differentiability, as seen in the inequality above, the challenge is to find a &delta-disc domain, centered at x0, that is small enough so that the graph of f over the domain lies between lines with slopes (f'(x0) + ε and (f'(x0) - ε).