csat-suneung 2026 Q13

csat-suneung · South-Korea · csat__math 4 marks Tangents, normals and gradients Geometric properties of tangent lines (intersections, lengths, areas)

For the function $f ( x ) = x ^ { 2 } - 4 x - 3$, let $l$ be the tangent line to the curve $y = f ( x )$ at the point $( 1 , - 6 )$, and for the function $g ( x ) = \left( x ^ { 3 } - 2 x \right) f ( x )$, let $m$ be the tangent line to the curve $y = g ( x )$ at the point $( 1,6 )$. What is the area of the figure enclosed by the two lines $l , m$ and the $y$-axis? [4 points]
(1) 21
(2) 28
(3) 35
(4) 42
(5) 49

For the function $f ( x ) = x ^ { 2 } - 4 x - 3$, let $l$ be the tangent line to the curve $y = f ( x )$ at the point $( 1 , - 6 )$, and for the function $g ( x ) = \left( x ^ { 3 } - 2 x \right) f ( x )$, let $m$ be the tangent line to the curve $y = g ( x )$ at the point $( 1,6 )$. What is the area of the figure enclosed by the two lines $l , m$ and the $y$-axis? [4 points]\\
(1) 21\\
(2) 28\\
(3) 35\\
(4) 42\\
(5) 49

Paper Questions

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