If for $f(x) = 2x - {x^2}$, Lagrange’s theorem satisfies in $[0, 1]$, then the value of $c \in [0,\,1]$ is

  • A

    $c = 0$

  • B

    $c = \frac{1}{2}$

  • C

    $c = \frac{1}{4}$

  • D

    $c = 1$

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