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Question Id : 18051 | Context : JEE Main 2026 (24 January Morning Shift)
Let \( \alpha, \beta \in \mathbb{R} \) be such that the function \( f(x)= \begin{cases} 2\alpha(x^2-2)+2\beta x, & x<1 \\ (\alpha+3)x+(\alpha-\beta), & x\ge 1 \end{cases} \) be differentiable at all \( x\in\mathbb{R} \). Then \( 34(\alpha+\beta) \) is equal to:


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