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Let f:[-1, 1] to R be defined as f(x)=ax...

Let `f:[-1, 1] to R` be defined as `f(x)=ax^(2)+bx+c` for all `x in [-1, 1]`, where `a, b, c in R` such that `f(-1)=2, f'(-1)=1` and for `x in (-1, 1) ` the maximum value of `f''(x)` is `(1)/(2)`. If `f(x) le alpha, x in [-1, 1]`, then the least value of `alpha` is equal to __________.

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