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Find the least value of k for which the ...

Find the least value of `k` for which the function `x^2+k x+1` is an increasing function in the interval (1,2)

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we have `f(x) =x^(2)+kx+1`
Now f(x) is increasing in (1,2)
`therefore f(x) gt0 forall` x in (1,2)
`rarr 2x+kge 0 forall` x in (1,2)
`rarr kge-2x forall` x in (1,2)
`rarr kge` greatest value of -2x in (1,2)
`rarr k ge-2`
Thus least value of K is -2
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