Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(\mathrm{x})= \begin{cases}2 \alpha\left(\mathrm{x}^2-2\right)+2 \beta \mathrm{x} & , \mathrm{x}

Question

Let $\alpha, \beta \in \mathbb{R}$ be such that the function $f(\mathrm{x})= \begin{cases}2 \alpha\left(\mathrm{x}^2-2\right)+2 \beta \mathrm{x} & , \mathrm{x}<1 \ (\alpha+3) \mathrm{x}+(\alpha-\beta) & , \mathrm{x} \geq 1\end{cases}$ be differentiable at all $x \in \mathbb{R}$. Then $34(\alpha+\beta)$ is equal to [JEE Main 2026, 24 Jan (Shift 1)]

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Let \(\alpha, \beta \in \mathbb{R}\) be such that the function \(f(\mathrm{x})= \begin{cases}2 \alpha\left(\mathrm{x}^2-…

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