Let f be a real-valued function with domain R [0,1]. If there is some K>0 such t

Question

Let f be a real-valued function with domain R [0,1]. If there is some K>0 such that f(x)-f(y) less than or equal to Klx-yl for all x and y in [0,1], which of the following must be true and why?

A. f is discontinuous at each point of (0,1)

B. f is not continuous on (0,1), but is discontinuous at only countably many points of (0,1).

C. f is continuous on (0,1), but differentiable at only countably many points of (0,1).

D. f is continuous on (0,1), but may not be differentiable on (0,1).

E. f is differentiable on (0,1).

Explanation / Answer

B. f is not continuous on (0,1), but is discontinuous at only countably many points of (0,1).

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