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Find the interval of monotonocity of the...

Find the interval of monotonocity of the function `f(x)=|x-1|x^2dot`

Text Solution

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`f(x)=(|x-1|/(x^2))={(1-x)/(2),xltxne`
`(x-1)/(x^(2)),xgt1`
Clearly f(x) is contiuous forall x in R except at x=0
`f(x)gt0rarrxlt0 "or" 1 lt xlt2`
f(x) `lt0rarrxrarr1 "or" xgt2`
Hence f(x) is increasing in `(-00)cup(1,2)` and decreasing in `(0,1)cup(2,00)`.
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