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Let f : R to R be a differentiable function given by f(x) =x^(3)-3x + 2020. If g(x) is a continuous function defined by g(x) ={{:("Minimum" f(t),0 le t le x, 0 le x le 1),("Maximum" f(t), 1 lt t le x, 1 lt x le 2):} and m and M be the least and the greatest value of g(x) on [0,2] then which one of the following is correct? |
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Answer» M-m=2 For `0 le x le 1`, f(x) is STRICTLY DECREASING `rArr g(x) =x^(2) - 3x + 2020, 0 le x le 1` For `1 lt x le 2`, f(x) is strictly increasing `rArr g(x) = xp^(3) - 3x + 2020, 1 lt x le 2` |
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