csat-suneung 2026 Q9

csat-suneung · South-Korea · csat__math 4 marks Tangents, normals and gradients Find tangent line with a specified slope or from an external point

For a positive number $a$, let the function $f ( x )$ be $$f ( x ) = x ^ { 3 } + 3 a x ^ { 2 } - 9 a ^ { 2 } x + 4$$ When the line $y = 5$ is tangent to the curve $y = f ( x )$, what is the value of $f ( 2 )$? [4 points]
(1) 11
(2) 12
(3) 13
(4) 14
(5) 15

For a positive number $a$, let the function $f ( x )$ be
$$f ( x ) = x ^ { 3 } + 3 a x ^ { 2 } - 9 a ^ { 2 } x + 4$$
When the line $y = 5$ is tangent to the curve $y = f ( x )$, what is the value of $f ( 2 )$? [4 points]\\
(1) 11\\
(2) 12\\
(3) 13\\
(4) 14\\
(5) 15

Paper Questions

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