Let f(x) be a real function which is continuous (see continuous function) on the interval [a,b] and differentiable on the interval (a,b). If f′(a) < K < f′(b) then there exists c in (a,b) such that f′(c) = K. This may appear to be a consequence of the intermediate value theorem, but no assumption is made that that f′(x) is itself continuous.