Differentiable function alpha beta (Jee Mains)

Continuity and Differentiability

Medium

Differentiable function alpha beta

Let α, β ∈ ${\Bbb R}$ be such that the function
f(x) $= \left\{ {\begin{array}{*{20}{c}} {2\alpha ({x^2} - 2) + 2\beta x}&{,x < 1}\\[0.9em] {(\alpha + 3)x + (\alpha - \beta )}&{,x \geqslant 1} \end{array}} \right.$
be differentiable at all x∈ ${\Bbb R}$ . Then 34(α + β) is equal to

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