The range of the polynomial $P(x)=4 x^3-3 x$ as $x$ varies over the interval $\left(-\frac{1}{2}, \frac{1}{2}\right)$ is

  • [KVPY 2016]
  • A

    $[-1,1]$

  • B

    $(-1,1]$

  • C

    $(-1,1)$

  • D

    $\left(-\frac{1}{2}, \frac{1}{2}\right)$

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  • [JEE MAIN 2022]