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

Question

\[\begin {array} {1 1} (a)\;\bigg[\frac{7}{8},\frac{5}{4}\bigg] & \quad (b)\;\bigg[\frac{1}{2},\frac{5}{8}\bigg] \\ (c)\;\bigg[\frac{1}{4},1\bigg] & \quad (d)\;\bigg[\frac{1}{4},\frac{1}{2}\bigg] \end {array}\]