Find the maximum and minimum value of \( \sin ^{6} x+\cos ^{6} x \). (a) 1 and \( \frac{1}{4} \)...

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Find the maximum and minimum value of \( \sin ^{6} x+\cos ^{6} x \).
(a) 1 and \( \frac{1}{4} \)
(b) 1 and \( \frac{3}{4} \)
(c) 0 and \( \frac{1}{4} \)
(d) 0 and \( \frac{3}{4} \)
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