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MathsJEE Main 24 Jan 2026, Shift 1·Q16·MCQ·Easy–moderate

Limits, Continuity & Differentiability · Differentiability of piecewise function

Let α,β∈R\alpha, \beta \in \mathbb{R} be such that the function f(x)={2α(x2−2)+2βx,x<1(α+3)x+(α−β),x≥1f(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∈Rx \in \mathbb{R}. Then 34(α+β)34(\alpha + \beta) is equal to
  1. (1)84
  2. (2)48
  3. (3)36
  4. (4)24

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