The following shows the graph of a continuous function $y = f ( x )$ and two distinct points $\mathrm { P } ( a , f ( a ) ) , \mathrm { Q } ( b , f ( b ) )$ on this graph. When the function $F ( x )$ satisfies $F ^ { \prime } ( x ) = f ( x )$, which of the following statements in $\langle$Remarks$\rangle$ are always correct? [4 points] $\langle$Remarks$\rangle$ ㄱ. The function $F ( x )$ is increasing on the interval $[ a , b ]$. ㄴ. $\frac { F ( b ) - F ( a ) } { b - a }$ is equal to the slope of line PQ. ㄷ. $\int _ { a } ^ { b } \{ f ( x ) - f ( b ) \} d x \leqq \frac { ( b - a ) \{ f ( a ) - f ( b ) \} } { 2 }$ (1) ㄱ (2) ㄴ (3) ㄱ, ㄷ (4) ㄴ, ㄷ (5) ㄱ, ㄴ, ㄷ
The following shows the graph of a continuous function $y = f ( x )$ and two distinct points $\mathrm { P } ( a , f ( a ) ) , \mathrm { Q } ( b , f ( b ) )$ on this graph.
When the function $F ( x )$ satisfies $F ^ { \prime } ( x ) = f ( x )$, which of the following statements in $\langle$Remarks$\rangle$ are always correct? [4 points]
$\langle$Remarks$\rangle$\\
ㄱ. The function $F ( x )$ is increasing on the interval $[ a , b ]$.\\
ㄴ. $\frac { F ( b ) - F ( a ) } { b - a }$ is equal to the slope of line PQ.\\
ㄷ. $\int _ { a } ^ { b } \{ f ( x ) - f ( b ) \} d x \leqq \frac { ( b - a ) \{ f ( a ) - f ( b ) \} } { 2 }$\\
(1) ㄱ\\
(2) ㄴ\\
(3) ㄱ, ㄷ\\
(4) ㄴ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ