Answer
$a.\quad $greatest, $7, 6,\ 5$
$b.\quad $smallest, $2, 4$
Work Step by Step
(a) A function value $f(a)$ is a local maximum value of $f$ if $f(a)$ is the $\fbox{greatest}$ value of $f$ on some open interval containing $a$.
From the graph of f we see that there are two local maximum values of $f$:
One local maximum is $\fbox{$7$}$, and it occurs when $x=2$;
the other local maximum is $\fbox{$6$}$, and it occurs when $x=\fbox{$5$}$ .
(b) The function value $f(a)$ is a local minimum value of f if $f(a)$ is the $\fbox{smallest}$ value of $f$ on some open interval
containing $a$. From the graph of $f$ we see that there is one local minimum value of $f.$
The local minimum value is $\fbox{$2$}$ , and it occurs when $x=\fbox{$4$} $.
