Let be such that the function f ( x ) = { 2 ( x 2 - 2 ) + 2 x , x 1 + 3 ) x , x 1 be differentiable at all x. Then 34 is equal to [2026]

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Solution

Q.
Let $α, β \in ℝ$ be such that the function $f (x)$ $=$ ${\begin{matrix} 2 α (x^{2} - 2) + 2 β x, & x < 1 \\ (α + 3) x + (α - β), & x \geq 1 \end{matrix}$

be differentiable at all $x \in ℝ$ . Then $34 (α + β)$ is equal to [2026]

1 84

2 24

3 36

4 48

Ans.
(4)

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