Let $f(t)$ be the piecewise linear function with domain $0t8$ shown in the graph below $($which is determined by connecting the dots$).$ Define a function $A(x)$ with domain $0x8$ by

$A(x)={\displaystyle \underset{0}{\overset{x}{}}}f(t)dt$

Notice that $A(x)$ is the net area under the function $f(t)$ for $0tx.$ If you click on the graph below, a full$-$size picture of the granh will onen in another window.

$($A$)$ Find the following values of the function $A(x).$

$]=[,\frac{?}{?}$# $]=[,$#$]=[,$#$]=[,$##$]=[,$##$]=[,$##$]=[,$##$]=[,$##$]=[,$##

$($B$)$ Use interval notation to indicate the interval or union of intervals where $A(x)$ is increasing and decreasing. $A(x)$ is increasing for $x$ in the interval $A(x)$ is decreasing for $x$ in the interval $$

$($C$)$ Find where $A(x)$ has its maximum and minimum values.

$A(x)$ has its maximum value when $x=$

$A(x)$ has its minimum value when $x=$