Solve the Problem $\mathrm { ft }$ ) of the Rocket Above the Ground (The Position Function)

Multiple Choice

Solve the problem.
-A rocket is launched straight up from level ground. The distance (in $\mathrm { ft }$ ) of the rocket above the ground (the position function) is $\mathrm { f } ( \mathrm { t } ) = 224 \mathrm { t } - 16 \mathrm { t } ^ { 2 }$ at any time $\mathrm { t }$ (in sec) . Find $\mathrm { f } ^ { \prime } ( 3 )$ and the initial velocity of the rocket.

A) $\mathrm { f } ^ { \prime } ( 3 ) = 224$ ; initial velocity $= 128 \mathrm { ft } / \mathrm { s }$
B) $\mathrm { f } ^ { \prime } ( 3 ) = 128$ ; initial velocity $= 224 \mathrm { ft } / \mathrm { s }$
C) $\mathrm { f } ^ { \prime } ( 3 ) = 528$ ; initial velocity $= 224 \mathrm { ft } / \mathrm { s }$
D) $f ^ { \prime } ( 3 ) = - 48$ ; initial velocity $= 224 \mathrm { ft } / \mathrm { s }$