[alamps3]

64) Suppose that f is a continuous real-valued function defined on the closed interval [0,1]. Which of the following must be true?
I. There is a constant C>0 st |f(x) - f(y)| <= C for all x and y in [0,1]
II. There is a constant D>0 st |f(x) - f(y)| <= 1 for all x and y in [0,1] that satisfy |x-y\<=D
III. There is a constant E>0 st |f(x) - f(y)| <= E|x-y| for all x, y in [0,1]

answer is I and II only.

Can someone provide a counterexample to 3 to show why it doesn't have to be true.