For the graph of $f(x)$ shown below, sketch two functions $F$ with $F'(x) = f(x)$. In one let $F(0) = 0$; in the other, let $F(0) = 1$. Mark $x_1$, $x_2$ and $x_3$ on the $x$-axis of your graph. Identify local maxima, minima and inflection points of $F(x)$.

(a) At which point does $F(x)$ achieve its largest value?

(b) At which point does $F(x)$ achieve its smallest value?

For the following questions, consider only the interior points on the domain on which $f(x)$ is shown.
(c) How many critical points does $F(x)$ have?

(d) How many local maxima does $F(x)$ have?

(e) How many local minima does $F(x)$ have?

(f) How many inflection points does $F(x)$ have?