csat-suneung 2013 Q15

csat-suneung · South-Korea · csat__math-humanities 4 marks Tangents, normals and gradients Determine unknown parameters from tangent conditions
The equation of the tangent line to the graph of the cubic function $f(x) = x^3 + ax^2 + 9x + 3$ at the point $(1, f(1))$ is $y = 2x + b$. What is the value of $a + b$? (Here, $a, b$ are constants.) [4 points]
(1) 1
(2) 2
(3) 3
(4) 4
(5) 5
The equation of the tangent line to the graph of the cubic function $f(x) = x^3 + ax^2 + 9x + 3$ at the point $(1, f(1))$ is $y = 2x + b$. What is the value of $a + b$? (Here, $a, b$ are constants.) [4 points]\\
(1) 1\\
(2) 2\\
(3) 3\\
(4) 4\\
(5) 5