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If ax^(3)-cx+bge0AAxepsilonR^(+)-{0} where a,b,cepsilonR^(+). Then the minimum value of ((27ab^(2))/(c^(3))) is………

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Solution :Let `F(X)=AX^(2)+B/x-C f^(')(x)=2ax-b/(x^(2))`
`f^(')(x)=0, x=(b/(2a))^(1/3)impliesa(b/(2a))^(2/3)+b/((b/(2a))^(1/3))gecimplies(27ab^(2))/(c^(3))ge4`


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