A piece of cardboard measures $35$ in$.$ by $56$ in$.$ Two equal squares are removed from the corners of a $35-$in$.$ side as shown in the figure. Two equal rectangles are removed from the other corners so that the tabs can be folded to form a rectangular box with lid. Complete parts $($a$)$ through $($d$).$

a$.$ Write a formula $V(x)$ for the volume of the box.

$V(x)=$

b$.$ Find the domain of $V$ for the problem situation and graph $V$ over this domain.

The domain is

$($Use interval notation. Use integers or fractions for any numbers in your expression.$)$

Choose the correct graph below.

A$.$

B$.$

B$.$

c$.$ Use a graphical method to find the maximum volume and the value of $x$ that gives it$.$

The maximum volume is $$ when $x=$

$($Round to the nearest whole number as needed.$)$

d$.$ Confirm your result in part $($c$)$ analytically.