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Q.

The least value of $k$ for which the function $x^{2} + k x + 1$ is an increasing function in the interval $1 < x < 2$ is

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answer is -2.

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Detailed Solution

$f' (x) = 2 x + k \geq 0 \forall x \in (1, 2) ∴ k + 2 \geq 0 a n d k + 4 \geq 0 ∴ k \geq - 2 \Rightarrow k_{m i n} = - 2$

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