Multiple Choice: The function $f$, whose graph consists of two line segments, is shown at right. Which of the following are true for $f$ on the open interval $\left(a, c\right)$?

1. The domain of the derivative of $f$ is the open interval $\left(a, c\right)$.

   Hint I:

   Is there anywhere within $a < x < c$ in which the derivative does not exist?

2. f is continuous on the open interval $\left(a, c\right)$.

   Hint II:

   Check all three conditions of continuity.

3. The derivative of $f$ is positive on the open interval $(b, c)$.

   Hint III:

   A positive derivative means that $f(x)$ is increasing.

1. I only

2. II only

3. III only

4. II & III only

5. I, II & III