If $f (x) = |x^{2} - 5 x + 6|, then f' (x)$ equals

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$2 x - 5 for 2 < x < 3$

$5 - 2 x for x < 3$

$2 x - 5 for x > 2$

$5 - 2 x for 2 < x < 3$

answer is B.

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Detailed Solution

$f (x) = |x^{2} - 5 x + 6| \Rightarrow f (x) = |(x - 2) (x - 3)|$
$i f 2 < x < 3 \Rightarrow f (x) = - (x - 2) (x - 3) = - (x^{2} - 5 x + 6) \Rightarrow f' (x) = - 2 x + 5$

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