Find an Equation for the Function $f ( x ) \text { whose derivative is } f ^ {t} ( x ) = 4 \sin ( 12 x ) \text { and }$

Multiple Choice

Find an equation for the function $f ( x ) \text { whose derivative is } f ^ {t} ( x ) = 4 \sin ( 12 x ) \text { and }$ whose graph passes through the point $\left( \frac { \pi } { 12 } , - \frac { 2 } { 3 } \right)$

A) $f ( x ) = - \frac { 1 } { 24 } \cos ( 3 x ) + 2$
B) $f ( x ) = - \frac { 1 } { 3 } \cos ( 12 x ) - 12$
C) $f ( x ) = \frac { 1 } { 6 } \cos ( 12 x ) + 1$
D) $f ( x ) = \frac { 1 } { 12 } \cos ( 24 x ) + 6$
E) $f ( x ) = - \frac { 1 } { 3 } \cos ( 12 x ) - 1$