It's just a minimum

Calculus Level 3

If \(a,b\) and \(c\) are constants satisfying the inequality \(ax^2 + \dfrac bx \geq c \), where \(x> 0 \), find the minimum vlaue of \( \dfrac{ab^2}{c^3} \).

If the minimum value can be expressed as \( \dfrac pq\), where \(p\) and \(q\) are coprime positive integers, submit your answer as \(p+q\).


This one of the old IIT question.
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