Find the interval of monotonocity of the function $f (x) = ln (x^{2} - 2 x) .$

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Solution

$f (x) = l n (x^{2} - 2 x)$

$f^{'} (x) = \frac{1}{x^{2} - 2 x} (2 x - 2)$

$= \frac{2 (x - 1)}{x (x - 2)}$

$\to$ function is strictly $↑$ es in $(0, 1) \cup (2, \infty)$

$\to$ function is strictly $↓$ es in $(- \infty, 0) \cup (1, 2)$

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