If \( a x^{2}+\frac{b}{x} \geq c \) for all positive \( x \), where \( a, b0 \), then (a) \( 27 ...

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If \( a x^{2}+\frac{b}{x} \geq c \) for all positive \( x \), where \( a, b0 \), then
(a) \( 27 a b^{2} \geq 4 c^{3} \)
(b) \( 27 a b^{2}4 c^{3} \)
(c) \( 4 a b^{2} \geq 27 c^{3} \)
(d) None of these
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