A quartic function $f ( x )$ with leading coefficient 1 satisfies the following conditions. (가) $f ^ { \prime } ( 0 ) = 0 , f ^ { \prime } ( 2 ) = 16$ (나) For some positive number $k$, $f ^ { \prime } ( x ) < 0$ on the two open intervals $( - \infty , 0 ) , ( 0 , k )$. Choose all correct statements from the following. [4 points] $\langle$Statements$\rangle$ ㄱ. The equation $f ^ { \prime } ( x ) = 0$ has exactly one real root in the open interval $( 0,2 )$. ㄴ. The function $f ( x )$ has a local maximum value. ㄷ. If $f ( 0 ) = 0$, then $f ( x ) \geq - \frac { 1 } { 3 }$ for all real numbers $x$. (1) ㄱ (2) ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
A quartic function $f ( x )$ with leading coefficient 1 satisfies the following conditions.\\
(가) $f ^ { \prime } ( 0 ) = 0 , f ^ { \prime } ( 2 ) = 16$\\
(나) For some positive number $k$, $f ^ { \prime } ( x ) < 0$ on the two open intervals $( - \infty , 0 ) , ( 0 , k )$.\\
Choose all correct statements from the following. [4 points]
$\langle$Statements$\rangle$\\
ㄱ. The equation $f ^ { \prime } ( x ) = 0$ has exactly one real root in the open interval $( 0,2 )$.\\
ㄴ. The function $f ( x )$ has a local maximum value.\\
ㄷ. If $f ( 0 ) = 0$, then $f ( x ) \geq - \frac { 1 } { 3 }$ for all real numbers $x$.\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ