For all functions $f ( x )$ that are differentiable on the set of all real numbers and satisfy the following conditions, what is the minimum value of $\int _ { 0 } ^ { 2 } f ( x ) d x$? [4 points] (가) $f ( 0 ) = 1 , f ^ { \prime } ( 0 ) = 1$ (나) If $0 < a < b < 2$, then $f ^ { \prime } ( a ) \leqq f ^ { \prime } ( b )$. (다) On the interval $( 0,1 )$, $f ^ { \prime \prime } ( x ) = e ^ { x }$. (1) $\frac { 1 } { 2 } e - 1$ (2) $\frac { 3 } { 2 } e - 1$ (3) $\frac { 5 } { 2 } e - 1$ (4) $\frac { 7 } { 2 } e - 2$ (5) $\frac { 9 } { 2 } e - 2$
For all functions $f ( x )$ that are differentiable on the set of all real numbers and satisfy the following conditions, what is the minimum value of $\int _ { 0 } ^ { 2 } f ( x ) d x$? [4 points]\\
(가) $f ( 0 ) = 1 , f ^ { \prime } ( 0 ) = 1$\\
(나) If $0 < a < b < 2$, then $f ^ { \prime } ( a ) \leqq f ^ { \prime } ( b )$.\\
(다) On the interval $( 0,1 )$, $f ^ { \prime \prime } ( x ) = e ^ { x }$.\\
(1) $\frac { 1 } { 2 } e - 1$\\
(2) $\frac { 3 } { 2 } e - 1$\\
(3) $\frac { 5 } { 2 } e - 1$\\
(4) $\frac { 7 } { 2 } e - 2$\\
(5) $\frac { 9 } { 2 } e - 2$