For all cubic functions $f ( x )$ satisfying $f ( 0 ) = 0$ and the following conditions, let $M$ be the maximum value and $m$ be the minimum value of $\frac { f ^ { \prime } ( 0 ) } { f ( 0 ) }$. What is the value of $M m$? [4 points] (가) The function $| f ( x ) |$ is not differentiable only at $x = - 1$. (나) The equation $f ( x ) = 0$ has at least one real root in the closed interval $[ 3,5 ]$. (1) $\frac { 1 } { 15 }$ (2) $\frac { 1 } { 10 }$ (3) $\frac { 2 } { 15 }$ (4) $\frac { 1 } { 6 }$ (5) $\frac { 1 } { 5 }$
For all cubic functions $f ( x )$ satisfying $f ( 0 ) = 0$ and the following conditions, let $M$ be the maximum value and $m$ be the minimum value of $\frac { f ^ { \prime } ( 0 ) } { f ( 0 ) }$. What is the value of $M m$? [4 points]\\
(가) The function $| f ( x ) |$ is not differentiable only at $x = - 1$.\\
(나) The equation $f ( x ) = 0$ has at least one real root in the closed interval $[ 3,5 ]$.\\
(1) $\frac { 1 } { 15 }$\\
(2) $\frac { 1 } { 10 }$\\
(3) $\frac { 2 } { 15 }$\\
(4) $\frac { 1 } { 6 }$\\
(5) $\frac { 1 } { 5 }$