Answer
$a) (a,0), (b,c)$
$b)(0,b)$
$c) x = 0\space and\space x = b$
Work Step by Step
a) The rate of change is positive when the slope of $f(x)$ is positive, that is, $f(x)$ is on an increasing trend.
$(a,0),(b,c)$
b) The rate of change is negative when the slope of $f(x)$ is negative, that is, $f(x)$ is on a diminishing trend.
$(0,b)$
c) The rate of change is $0$ when the slope of $f(x)$ is $0$, that is, $f(x)$'s trend is stable.
$\{0,b\}$
