Function $f (x) = x^{3} - 3 x^{2} - 9 x + 22$ is monotonic decreasing for

- 1 < x < 3

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1 < x < 3

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- 3 < x < 1

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None of these

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Solution

The correct option is A $- 1 < x < 3$
$f (x) = x^{3} - 3 x^{2} - 9 x + 22$
Given $f$ is monotonic decreasing, so $f^{'} (x) < 0$
$f (x) = 3 x^{2} - 6 x - 9 < 0$
$\Rightarrow x^{2} - 2 x - 3 < 0$
$\Rightarrow - 1 < x < 3$

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