Calculus Level 2

$f(x)=\begin{cases} -3ax^2-2 \ \ , \quad x<1 \\ bx+a^2 \ \quad \ \ , \quad x \geq 1 \end{cases}$ 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.

×