csat-suneung 2014 Q30

csat-suneung · South-Korea · csat__math-B 4 marks Second order differential equations Verifying a particular solution satisfies a second-order ODE

For a quadratic function $f ( x )$, the function $g ( x ) = f ( x ) e ^ { - x }$ satisfies the following conditions. (가) The points $( 1 , g ( 1 ) )$ and $( 4 , g ( 4 ) )$ are inflection points of the curve $y = g ( x )$. (나) The number of tangent lines drawn from the point $( 0 , k )$ to the curve $y = g ( x )$ is 3 when $k$ is in the range $- 1 < k < 0$. Find the value of $g ( - 2 ) \times g ( 4 )$. [4 points]

For a quadratic function $f ( x )$, the function $g ( x ) = f ( x ) e ^ { - x }$ satisfies the following conditions.\\
(가) The points $( 1 , g ( 1 ) )$ and $( 4 , g ( 4 ) )$ are inflection points of the curve $y = g ( x )$.\\
(나) The number of tangent lines drawn from the point $( 0 , k )$ to the curve $y = g ( x )$ is 3 when $k$ is in the range $- 1 < k < 0$.\\
Find the value of $g ( - 2 ) \times g ( 4 )$. [4 points]

Paper Questions

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