The graph of $$a continuous function f$$is $$shown$.$ The three regions between the graph of$$f $$and the x$-$axis are marked A$,$B$,$and C$,$and have unsigned areas $5\mathrm{.}5,4,$and $15\mathrm{.}5,$respectively$.$ Let F$($x$)$be$$an $$antiderivative of$$f $$that is $$differentiable on$(0,4)$and $$with F$(1)=8.$

$($a$)$Find F$(0)$and F$(4).$

F$(0)=$

F$(4)=$

$($b$)$What is $$the minimum number of $$times F $$equals $5$on $$the interval $[0,4]?$

$$

$($c$)$Find all intervals where F$$is $$increasing$.($Enter $$your answer using interval notation.$)$

$$

Justify your answer.

F$$is $$increasing where F$($x$)>0.$F$$is $$increasing where f$($x$)$is $$concave upward.

F$$is $$increasing where f$($x$)>0.$

F$$is $$increasing where F$($x$)$is $$concave upward.

F$$is $$increasing where f$($x$)$is $$increasing$.$