Answer
If the derivative of a function is constant, the function is linear (it has the form$\quad f(x)=mx+b\quad)$
Work Step by Step
Let's find a function whose derivative is a constant, $a$.
$f(x)=ax$
If another function is such that $g'(x)=a$, then
by Corollary 2, it follows that $g(x)=f(x)+C$
where $C$ is some constant.
So, if the derivative of a function is constant, it has the form $g(x)=ax+C$, which is a linear function (has a straight line as a graph).
The choice of the constant $a$ was arbitrary, so we can conclude:
If the derivative of a function is constant, the function is linear $(f(x)=mx+b)$
