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Q.

The function f(x)=|x−1|x2

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a

increase in (−∞,0)∪(1,2)

b

increase in (0,1)∪(2,∞)

c

decrease in (0,1)∪(2,∞)

d

decrease in (−∞,∞)∪(1,2)

answer is A.

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Detailed Solution

f(x)=|x−1|x2=x−1x2,x≥11−xx2,x<1,x≠0∴f'(x)=x−2x3,x<1,x≠0does not exist, x=12−xx3,x>1clearly, f'(x)>0 for x<0 or 12thus, f(x) is increasing for (−∞,0)∪(1,2) and decreasing for (0,1)∪(2,∞)The correct option is (1) and (3)
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The function f(x)=|x−1|x2