The least value of \( \alpha \in R \) for which \( 4 \alpha x^{2}+\frac{1}{x} \geq 1 \), for all...

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The least value of \( \alpha \in R \) for which \( 4 \alpha x^{2}+\frac{1}{x} \geq 1 \), for all \( x0 \) is \( x0 \), is
[One Correct Option 2016 Adv.]
(a) \( \frac{1}{64} \)
(b) \( \frac{1}{32} \)
(c) \( \frac{1}{27} \)
(d) \( \frac{1}{25} \)
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