# 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 $$p+q$$.

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