CPM Homework Help : APCALC Problem 8-73

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 $(a,c)$ ?

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

I only

II only

III only

II & III only

I, II, & III

Hint I:

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

Hint II:

Check all three conditions of continuity.

Hint III:

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