Cooper Section $8\mathrm{.}5\backslash$#$1$

Let $\backslash ($ A$($r$)\backslash )$ be the area in square meters enclosed by a circle of radius $\backslash ($ r $\backslash )$ meters.

a$.$ What are the units of $\backslash ($ A$^\{\backslash$prime$\}($r$)\backslash )?$

A$.$ meters per minute

B$.$ meters

C$.$ cubic meters

D$.$ square meters

b$.$ What is the meaning of the statement that $\backslash ($ A$^\{\backslash$prime$\}(3)=6\backslash$pi $\backslash )?$

A$.$ The area increases by $3$ square meters whenever the radius is increased by $[6`\backslash (\backslash$backslash $\backslash )$ pi $\backslash (\backslash$backslash $\backslash ))$ meters.

B$.$ When the radius is $\backslash (6\backslash$pi $\backslash )$ meters, the area is increasing at a rate of $3$ square meters per meter of radius.

C$.$ The area increases by $\backslash (6\backslash$pi $\backslash )$ square meters whenever the radius is increased by three meters.

D$.$ The area increases by $\backslash (6\backslash$pi $\backslash )$ square meters whenever the radius is increased by one meter.

E$.$ The area increases by $3$ square meters whenever the radius is increased by one meter.

F$.$ When the radius is $3$ meters, the area is increasing at a rate of $\backslash (6\backslash$pi $\backslash )$ square meters per three meters of radius.

G$.$ When the radius is $3$ meters, the area is increasing at a rate of $\backslash (6\backslash$pi $\backslash )$ square meters per meter of radius.