$\text { Find the vectors } \mathbf { r } ( t ) \text { and } \mathbf { r } ^ { t } ( t ) \text { for the following vector function. }$

Multiple Choice

$\text { Find the vectors } \mathbf { r } ( t ) \text { and } \mathbf { r } ^ { t } ( t ) \text { for the following vector function. }$ $\mathbf { r } ( t ) = ( 1 + 2 t ) \mathbf { i } + \left( 2 + 5 t ^ { 2 } \right) \mathbf { j } + 2 \mathbf { k }$

A) $\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 18 \mathbf { i } + 30 \mathbf { j }$
B) $\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }$
C) $\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 4 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }$
D) $\mathbf { r } ( 3 ) = 7 \mathbf { i } + 2 \mathbf { j } + 47 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 30 \mathbf { j }$
E) $\mathbf { r } ( 3 ) = 7 \mathbf { i } + 47 \mathbf { j } + 2 \mathbf { k } , \mathbf { r } ^ { \prime } ( 3 ) = 2 \mathbf { i } + 90 \mathbf { j }$