Solve the Problem $\mathrm { f } ( \mathrm { t } ) = 4 + 130 \mathrm { t } - 4.9 \mathrm { t } ^ { 2 }$

Solve the problem.
-An arrow is shot straight up from level ground. The distance (in meters) of the arrow above the ground (the position function) is $\mathrm { f } ( \mathrm { t } ) = 4 + 130 \mathrm { t } - 4.9 \mathrm { t } ^ { 2 }$ at any time $\mathrm { t }$ (in sec) . Find $\mathrm { f } ^ { \prime } ( 1 )$ and the initial velocity of the arrow.

A) $\mathrm { f } ^ { \prime } ( 1 ) = 120.2$ ; initial velocity $= 130 \mathrm {~m} / \mathrm { s }$
B) $\mathrm { f } ^ { \prime } ( 1 ) = 124.2$ ; initial velocity $= 130 \mathrm {~m} / \mathrm { s }$
C) $f ^ { \prime } ( 1 ) = 120.2$ ; initial velocity $= 4 \mathrm {~m} / \mathrm { s }$
D) $f ^ { \prime } ( 1 ) = - 9.8$ ; initial velocity $= 130 \mathrm {~m} / \mathrm { s }$

Correct Answer:

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