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Find the least value of ' a ' such that ...

Find the least value of `' a '` such that the function `f(x)=x^2+a x+1` is increasing on `[1,\ 2]` . Also, find the greatest value of `' a '` for which `f(x)` is decreasing on `[1,\ 2]` .

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If yR' is the least value of 'a' such that the function f(x) = x^(2) + ax +1 is increasing on [1, 2] and 'S' is the greatest value of ' a' such that the function f(x) = x^(2) + ax +1 is decreasing on [1, 2], then the value of |R — S| is_____________