JEE-Advanced 2015 (19.B/40)

$f(x)=\begin{cases} -3ax^2-2 \ \ , \quad x<1 \\ bx+a^2 \ \quad \ \ , \quad x \geq 1 \end{cases}$ Let $a$ and $b$ be real numbers such that the above function $f(x)$ is differentiable for all real $x$ , then find the possible value(s) of $a$ . \[\begin{array}{} (1) \, 1 \quad \quad \quad \quad \quad \quad \quad \quad & (2) \, 2 \\ (3) \, 3 & (4) \, 4 \end{array}\]
Note :

• Submit your answer as the increasing order of the serial numbers of all the correct options.

• For eg, if your answer is $(1),(2)$ , then submit 12 as the correct answer, if your answer is $(2),(3),(4)$ , then submit 234 as the correct answer.