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Let f(x) = Max. {x^2, (1 - x)^2, 2x(1 -...

Let f(x) = Max. `{x^2, (1 - x)^2, 2x(1 - x)} where x in [0, 1]` If Rolle's theorem is applicable for f(x) on largestpossible interval [a, b] then the value of `2(a+b+c)` when `c in [a, b]` such that f'(c) = 0, is

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