JEE-Advanced 2015 (19.B/40)

Calculus Level 3

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

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