csat-suneung 2013 Q18

csat-suneung · South-Korea · csat__math-humanities 4 marks Implicit equations and differentiation Piecewise differentiability and continuity conditions
The function $$f(x) = \begin{cases} x^3 + ax & (x < 1) \\ bx^2 + x + 1 & (x \geq 1) \end{cases}$$ is differentiable at $x = 1$. What is the value of $a + b$? (Here, $a, b$ are constants.) [4 points]
(1) 5
(2) 6
(3) 7
(4) 8
(5) 9
The function
$$f(x) = \begin{cases} x^3 + ax & (x < 1) \\ bx^2 + x + 1 & (x \geq 1) \end{cases}$$
is differentiable at $x = 1$. What is the value of $a + b$?\\
(Here, $a, b$ are constants.) [4 points]\\
(1) 5\\
(2) 6\\
(3) 7\\
(4) 8\\
(5) 9