The function $f$ graphed below $is$ defined $by$ a polynomial expression $of$ degree $4.$ Use the graph $to$ solve the exercise.

$(a)$ A function value $f(a)is$ a local maximum value $offiff(a)is$ the $(smallestor$ largest$)$

value $offon$ some open interval containing

$a.$ From the graph $offwe$ see that there are two local maximum values $off$ : one local maximum $is$

$,$ and $it$

occurs when $x=2$; the other local maximum $is$

$,$ and $it$ occurs when $x=$

$.$

$(b)$ The function value $f(a)is$ a local minimum value $offiff(a)is$ the $(smallestor$ largest$)$

value $offon$ some open interval containing

$a.$ From the graph $offwe$ see that there $is$ one local minimum value $off.$ The local minimum value $is$

$,$ and $it$

occurs when $x=$

$.$