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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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To find the least value of \( k \) for which the function \( f(x) = x^2 + kx + 1 \) is an increasing function in the interval \( (1, 2) \), we need to analyze the derivative of the function. ### Step-by-Step Solution: 1. **Find the derivative of the function**: \[ f'(x) = \frac{d}{dx}(x^2 + kx + 1) = 2x + k \] ...
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