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) $f ( x ) = - \frac { 1 } { 3 } \cos ( 12 x ) - 1$

Question

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) $f ( x ) = - \frac { 1 } { 3 } \cos ( 12 x ) - 1$

Quizplus · Accepted Answer

The antiderivative of $4 \sin(12x)$ is $-\frac{1}{3} \cos(12x) + C$. Using the point $\left( \frac{\pi}{12}, -\frac{2}{3} \right)$, we find $C = -1$.

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

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