If $f(x) = \sin^6 x + \cos^6 x$ for $x \in R$,then $f(x)$ lies in the interval

  • A
    $\left[\frac{7}{8}, \frac{5}{4}\right]$
  • B
    $\left[\frac{1}{2}, \frac{5}{8}\right]$
  • C
    $\left[\frac{1}{4}, 1\right]$
  • D
    $\left[\frac{1}{4}, \frac{1}{2}\right]$

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