$\text { Find the function } y = f ( t ) \text { passing through the point } ( 0,15 ) \text { with the first derivative }$ $\frac { d y } { d t } = \frac { 1 } { 4 } t .$
A)$y ( t ) = \frac { t ^ { 2 } } { 8 } + 15$
B) $y ( t ) = 8 t ^ { 2 } + 15$
C) $y ( t ) = 4 t + 15$
D) $y ( t ) = \frac { t ^ { 2 } } { 4 } + 15$
E) $y ( t ) = \frac { t } { 4 } + 15$

Question

Quizplus · Accepted Answer

To find $y(t)$, integrate the given derivative $\frac{dy}{dt} = \frac{1}{4}t$ to get $y(t) = \frac{1}{8}t^2 + C$. Using the point (0,15), we find $C = 15$, so $y(t) = \frac{t^2}{8} + 15$.

Find the function y=f(t) passing through the point (0,15) with the first derivative \text { Find the function } y = f ( t ) \text { passing through the point } ( 0,15 ) \text { with the first derivative } Find the function y=f(t) passing through the point (0,15) with the first derivative

$\text { Find the function } y = f ( t ) \text { passing through the point } ( 0,15 ) \text { with the first derivative }$