Ques. Let F be real valued function with domain [0,1]. if there is some K > 0 such that

f(x) - f(y) <= K |x-y| for all x and y in [0,1], which of the following will be true ?

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

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

C) f is continuous on (0,1)but it is 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)

Please explain your answer. Thanks