csat-suneung 2016 Q28

csat-suneung · South-Korea · csat__math-A 4 marks Tangents, normals and gradients Find tangent line equation at a given point

Two polynomial functions $f ( x ) , g ( x )$ satisfy the following conditions. (가) $g ( x ) = x ^ { 3 } f ( x ) - 7$ (나) $\lim _ { x \rightarrow 2 } \frac { f ( x ) - g ( x ) } { x - 2 } = 2$
When the equation of the tangent line to the curve $y = g ( x )$ at the point $( 2 , g ( 2 ) )$ is $y = a x + b$, find the value of $a ^ { 2 } + b ^ { 2 }$. (where $a , b$ are constants.) [4 points]

Two polynomial functions $f ( x ) , g ( x )$ satisfy the following conditions.\\
(가) $g ( x ) = x ^ { 3 } f ( x ) - 7$\\
(나) $\lim _ { x \rightarrow 2 } \frac { f ( x ) - g ( x ) } { x - 2 } = 2$

When the equation of the tangent line to the curve $y = g ( x )$ at the point $( 2 , g ( 2 ) )$ is $y = a x + b$, find the value of $a ^ { 2 } + b ^ { 2 }$.\\
(where $a , b$ are constants.) [4 points]

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