Let \( \alpha=\sum_{k=1}^{\infty} \sin ^{2 k}\left(\frac{\pi}{6}\right) \) Let \( g:[0,1] \right...

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Let \( \alpha=\sum_{k=1}^{\infty} \sin ^{2 k}\left(\frac{\pi}{6}\right) \)
Let \( g:[0,1] \rightarrow r \) be the function defined by \( g(x)=2^{\alpha x}+2^{\alpha(1-x)} \)
Then, which of the following statements is/are TRUE?
(a) The minimum value of \( g(x) \) is \( 2^{7 / 6} \)
(b) The maximum value of \( \mathrm{g}(x) \) is \( 1+2^{1 / 3} \)
(c) The function \( g(x) \) attains its maximum at more than one point
(d) The function \( g(x) \) attains its minimum at more than one point
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