The function $f (x) = 5 + 36 x + 3 x^{2} - 2 x^{3}$ is increasing in the interval

(- 2, 3)

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(2, 3)

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[2, - 3)

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(2, 3]

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Solution

The correct option is A $(- 2, 3)$
$f (x) = 5 + 36 x + 3 x^{2} - 2 x^{3}$
$∴ f^{^{'}} (x) = - 6 x^{2} + 6 x + 36$
$= - 6 (x^{2} - x - 6)$
$= - 6 (x - 3) (x + 2) > 0 [$ for increasing function]
$\Rightarrow (x - 3) (x + 2) < 0 \Rightarrow - 2 < x < 3$

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(a)

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