In the interval (1, 2), function f(x) = 2 | x − 1 | + 3 | x − 2 | is

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decreasing 	ext { Given }: f\left( x ight) = 2\left| x - 1 ight| + 3\left| x - 2 ight| 	ext { If 1 < x < 2, then }\left| x - 1 ight| = x - 1 . \Rightarrow \left| x - 2 ight| = - \left( x - 2 ight) 	ext { Now,} f\left( x ight) = 2\left| x - 1 ight| + 3\left| x - 2 ight| = 2 \left( x - 1 ight) + 3 \left( - x + 2 ight) = 2x - 2 - 3x + 6 = - x + 4 f'\left( x ight) = - 1 < 0 	ext { So,}f\left( x ight) 	ext { is decreasing when 1 < x < 2 } .

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