For a function $f ( x )$ that is differentiable on $x > 0$, $$f ^ { \prime } ( x ) = 2 - \frac { 3 } { x ^ { 2 } } , \quad f ( 1 ) = 5$$ For a function $g ( x )$ that is differentiable on $x < 0$ and satisfies the following conditions, what is the value of $g ( - 3 )$? [4 points] (가) For all real numbers $x < 0$, $g ^ { \prime } ( x ) = f ^ { \prime } ( - x )$. (나) $f ( 2 ) + g ( - 2 ) = 9$
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5

For a function $f ( x )$, if $f ^ { \prime } ( x ) = 4 x ^ { 3 } - 2 x$ and $f ( 0 ) = 3$, what is the value of $f ( 2 )$? [3 points]

Let $I ( x ) = \int \frac { 6 } { \sin ^ { 2 } x ( 1 - \cot x ) ^ { 2 } } d x$. If $I ( 0 ) = 3$, then $I \left( \frac { \pi } { 12 } \right)$ is equal to
(1) $2 \sqrt { 3 }$
(2) $\sqrt { 3 }$
(3) $3 \sqrt { 3 }$
(4) $6 \sqrt { 3 }$

Q73. Let $I ( x ) = \int \frac { 6 } { \sin ^ { 2 } x ( 1 - \cot x ) ^ { 2 } } d x$. If $I ( 0 ) = 3$, then $I \left( \frac { \pi } { 12 } \right)$ is equal to
(1) $2 \sqrt { 3 }$
(2) $\sqrt { 3 }$
(3) $3 \sqrt { 3 }$
(4) $6 \sqrt { 3 }$

Given that
$$\frac { d y } { d x } = 3 x ^ { 2 } - \frac { 2 - 3 x } { x ^ { 3 } } , \quad x \neq 0$$
and $y = 5$ when $x = 1$, find $y$ in terms of $x$.
A $y = \frac { 1 } { 3 } x ^ { 3 } + x ^ { - 2 } - 3 x ^ { - 1 } + 6 \frac { 2 } { 3 }$
B $y = x ^ { 3 } + \frac { 1 } { 2 } x ^ { - 2 } - 3 x ^ { - 1 } + 6 \frac { 1 } { 2 }$
C $y = x ^ { 3 } + x ^ { - 2 } - 3 x ^ { - 1 } + 6$
D $y = x ^ { 3 } + x ^ { - 2 } - x ^ { - 1 } + 4$
E $y = x ^ { 3 } + 2 x ^ { - 2 } - x ^ { - 1 } + 3$
F $y = 3 x ^ { 3 } + x ^ { - 2 } - x ^ { - 1 } + 2$