The set of values $x$ for which $f (x) = x^{3} - 6 x^{2} + 27 x + 10$ is increasing is

(1, 2)

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(- \infty, 1) U (2, \infty)

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(- \infty, \infty)

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(- \infty, 1)

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Solution

The correct option is C $(- \infty, \infty)$
$f^{'} (x) = 3 x^{2} - 12 x + 27$
$= 3 (x^{2} - 4 x + 9)$
$= 3 ((x - 2)^{2} + 5)$
$f^{'} (x)$ is always $+ i v e$ for $\forall x ϵ R$

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