csat-suneung 2013 Q19

csat-suneung · South-Korea · csat__math-science 4 marks Stationary points and optimisation Analyze function behavior from graph or table of derivative
A cubic function $f ( x )$ satisfies $f ( 0 ) > 0$. Define the function $g ( x )$ as
$$g ( x ) = \left| \int _ { 0 } ^ { x } f ( t ) d t \right|$$
The graph of the function $y = g ( x )$ is as shown in the figure. Which of the following statements are correct? Choose all that apply. [4 points]
ㄱ. The equation $f ( x ) = 0$ has three distinct real roots. ㄴ. $f ^ { \prime } ( 0 ) < 0$ ㄷ. The number of natural numbers $m$ satisfying $\int _ { m } ^ { m + 2 } f ( x ) d x > 0$ is 3.
(1) ㄴ
(2) ㄷ
(3) ㄱ, ㄴ
(4) ㄱ, ㄷ
(5) ㄱ, ㄴ, ㄷ
A cubic function $f ( x )$ satisfies $f ( 0 ) > 0$. Define the function $g ( x )$ as

$$g ( x ) = \left| \int _ { 0 } ^ { x } f ( t ) d t \right|$$

The graph of the function $y = g ( x )$ is as shown in the figure.\\
Which of the following statements are correct? Choose all that apply. [4 points]

\section*{<Remarks>}
ㄱ. The equation $f ( x ) = 0$ has three distinct real roots.\\
ㄴ. $f ^ { \prime } ( 0 ) < 0$\\
ㄷ. The number of natural numbers $m$ satisfying $\int _ { m } ^ { m + 2 } f ( x ) d x > 0$ is 3.\\
(1) ㄴ\\
(2) ㄷ\\
(3) ㄱ, ㄴ\\
(4) ㄱ, ㄷ\\
(5) ㄱ, ㄴ, ㄷ