csat-suneung 2021 Q9

csat-suneung · South-Korea · csat__math-humanities 3 marks Tangents, normals and gradients Normal or perpendicular line problems
The tangent line to the curve $y = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ at point $\mathrm { A } ( 0,2 )$ is perpendicular to a line passing through point A. What is the $x$-intercept of this line? [3 points]
(1) 4
(2) 6
(3) 8
(4) 10
(5) 12
The tangent line to the curve $y = x ^ { 3 } - 3 x ^ { 2 } + 2 x + 2$ at point $\mathrm { A } ( 0,2 )$ is perpendicular to a line passing through point A. What is the $x$-intercept of this line? [3 points]\\
(1) 4\\
(2) 6\\
(3) 8\\
(4) 10\\
(5) 12