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JEE MainMathematicsModerateApplication of derivatives

Let $f(x) = x^{3} + 6x^{2} + ax + 2\.\ If\ ( - 3, - 1)$ is the
largest possible open interval in which f(x) is a decreasing function,
then the value of must be

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Source: Grass-G / M-28 Mathematics Paper FST 16 Jan.docx

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