Question

5. (3 points) Which of the following statements best describes the relationship between continuity and differentiability for a function? Choose only one, and assume that the functions are defined for all real numbers. (A) A function must be both differentiable and continuous at r = a or neither; you cannot have one without the other. (B) If a function is differentiable at I = a then it must also be continuous at r = a. (C) If a function is continuous at r= a then it must also be differentiable at r=a. (D) There is at least one function that is continuous for some r = a where it is not differentiable, and at least one other function that is differentiable at some r = a where it is not continuous. (E) Two of the above statements mean the same thing, and are both the correct choice.