For the problem below, can you explain in details why answer #3 is wrong?

10. Let / be a function such that lim 5. Which of the following must be true? 1. f is continuous at x = 2 II. / is differentiable at = 2. Ill. The derivative of f is continuous at x - 1. A) Ionly 10 1 only I and II only DJ I and III only [) II and Ill only