For the function $f ( x ) = 2 x \cos x$ with domain $\{ x \mid 0 \leq x \leq \pi \}$, which of the following are correct? Choose all that apply from . [4 points] Remarks ㄱ. If $f ^ { \prime } ( a ) = 0$, then $\tan a = \frac { 1 } { a }$. ㄴ. There exists $a$ in the interval $\left( \frac { \pi } { 4 } , \frac { \pi } { 3 } \right)$ where the function $f ( x )$ has a local maximum value at $x = a$. ㄷ. On the interval $\left[ 0 , \frac { \pi } { 2 } \right]$, the number of distinct real roots of the equation $f ( x ) = 1$ is 2. (1) ㄱ (2) ㄷ (3) ㄱ, ㄴ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
For the function $f ( x ) = 2 x \cos x$ with domain $\{ x \mid 0 \leq x \leq \pi \}$, which of the following are correct? Choose all that apply from <Remarks>. [4 points]
\textbf{Remarks}\\
ㄱ. If $f ^ { \prime } ( a ) = 0$, then $\tan a = \frac { 1 } { a }$.\\
ㄴ. There exists $a$ in the interval $\left( \frac { \pi } { 4 } , \frac { \pi } { 3 } \right)$ where the function $f ( x )$ has a local maximum value at $x = a$.\\
ㄷ. On the interval $\left[ 0 , \frac { \pi } { 2 } \right]$, the number of distinct real roots of the equation $f ( x ) = 1$ is 2.\\
(1) ㄱ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ