csat-suneung 2020 Q30

csat-suneung · South-Korea · csat__math-humanities 4 marks Stationary points and optimisation Determine parameters from given extremum conditions

A cubic function $f ( x )$ with positive leading coefficient satisfies the following conditions. (가) The equation $f ( x ) - x = 0$ has exactly 2 distinct real roots. (나) The equation $f ( x ) + x = 0$ has exactly 2 distinct real roots. When $f ( 0 ) = 0$ and $f ^ { \prime } ( 1 ) = 1$, find the value of $f ( 3 )$. [4 points]

A cubic function $f ( x )$ with positive leading coefficient satisfies the following conditions.\\
(가) The equation $f ( x ) - x = 0$ has exactly 2 distinct real roots.\\
(나) The equation $f ( x ) + x = 0$ has exactly 2 distinct real roots.\\
When $f ( 0 ) = 0$ and $f ^ { \prime } ( 1 ) = 1$, find the value of $f ( 3 )$. [4 points]

Paper Questions

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