Ques: 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 such that |f(x) -f(y)| <= C for all x and y in [0,1]

II. There is a constant D > 0 such that |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 such that |f(x) -f(y)| <= E |x-y| for all x and y in [0,1]

A) I only

B) III only

C) I & II only

D) II & III only

E) I, II * III only

Any general method of solving such problems ?

Thanks.