If f(x)=x2−5x+6, then f'(x) equals

A
$2 x - 5 for 2 < x < 3$
B
$5 - 2 x for 2 < x < 3$
C
$2 x - 5 for x > 2$
D
$5 - 2 x for x < 3$

Solution:

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

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

Solution:

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