Let $f(x)={{x}^{2}}-x+k-2,k\in R$ then the complete set of values of $k$ for which $y=\left| f\left( \left| x \right| \right) \right|$ is non-derivable at $5$ distinict points is 

  • A

    $(1,4)$

  • B

    $\left( 0,\frac{9}{4} \right)$

  • C

    $\left( -\infty ,2 \right)$

  • D

    $\left( 2,\frac{9}{4} \right)$

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