For a quartic function $f ( x )$ with leading coefficient 1, the function $g ( x )$ satisfies the following conditions. (가) When $- 1 \leqq x < 1$, $g ( x ) = f ( x )$. (나) For all real numbers $x$, $g ( x + 2 ) = g ( x )$. Which of the following statements in are correct? [4 points] Remarks ㄱ. If $f ( - 1 ) = f ( 1 )$ and $f ^ { \prime } ( - 1 ) = f ^ { \prime } ( 1 )$, then $g ( x )$ is differentiable on the entire set of real numbers. ㄴ. If $g ( x )$ is differentiable on the entire set of real numbers, then $f ^ { \prime } ( 0 ) f ^ { \prime } ( 1 ) < 0$. ㄷ. If $g ( x )$ is differentiable on the entire set of real numbers and $f ^ { \prime } ( 1 ) > 0$, then there exists $c$ in the interval $( - \infty , - 1 )$ such that $f ^ { \prime } ( c ) = 0$. (1) ᄀ (2) ᄂ (3) ᄀ, ᄃ (4) ㄴ,ㄷ (5) ᄀ, ᄂ, ᄃ
For a quartic function $f ( x )$ with leading coefficient 1, the function $g ( x )$ satisfies the following conditions.\\
(가) When $- 1 \leqq x < 1$, $g ( x ) = f ( x )$.\\
(나) For all real numbers $x$, $g ( x + 2 ) = g ( x )$.
Which of the following statements in <Remarks> are correct? [4 points]
\textbf{Remarks}\\
ㄱ. If $f ( - 1 ) = f ( 1 )$ and $f ^ { \prime } ( - 1 ) = f ^ { \prime } ( 1 )$, then $g ( x )$ is differentiable on the entire set of real numbers.\\
ㄴ. If $g ( x )$ is differentiable on the entire set of real numbers, then $f ^ { \prime } ( 0 ) f ^ { \prime } ( 1 ) < 0$.\\
ㄷ. If $g ( x )$ is differentiable on the entire set of real numbers and $f ^ { \prime } ( 1 ) > 0$, then there exists $c$ in the interval $( - \infty , - 1 )$ such that $f ^ { \prime } ( c ) = 0$.\\
(1) ᄀ\\
(2) ᄂ\\
(3) ᄀ, ᄃ\\
(4) ㄴ,ㄷ\\
(5) ᄀ, ᄂ, ᄃ