csat-suneung 2022 Q10

csat-suneung · South-Korea · csat__math 4 marks Tangents, normals and gradients Determine unknown parameters from tangent conditions

For a cubic function $f ( x )$, the tangent line to the curve $y = f ( x )$ at the point $( 0,0 )$ and the tangent line to the curve $y = x f ( x )$ at the point $( 1,2 )$ coincide. What is the value of $f ^ { \prime } ( 2 )$? [4 points]
(1) $-18$
(2) $-17$
(3) $-16$
(4) $-15$
(5) $-14$

For a cubic function $f ( x )$, the tangent line to the curve $y = f ( x )$ at the point $( 0,0 )$ and the tangent line to the curve $y = x f ( x )$ at the point $( 1,2 )$ coincide. What is the value of $f ^ { \prime } ( 2 )$? [4 points]\\
(1) $-18$\\
(2) $-17$\\
(3) $-16$\\
(4) $-15$\\
(5) $-14$

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