Continuous Bounded Derivative

If f(x) has a continuous bounded derivative(say M is a bound), then f(x) - f(y) = f'(c)(x-y) for some c in (x,y), taking absolute values yields |f(x) - f(y)| <= M|x-y|, so f is Lipschitz of order one.

Random yes, but Lipschitz is fun to say!