Find the intervals of monotonicity of the function
xlogx
A
Increasing in (0,e)
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B
Increasing in (e,∞)
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C
decreasing in (0,e)−{1}
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D
Decreasing in (e,∞)
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Solution
The correct options are B Increasing in (e,∞) C decreasing in (0,e)−{1} Let f(x)=xlogx∴ Domain of f is (0,∞)−{1} Now f′(x)=logx−1(logx)2 For f to be increasing f′(x)>0⇒logx−1>0⇒x>e and for f to be decresing, f′(x)<0⇒logx−1<0⇒x<e also x>0≠1⇒xϵ(0,e)−{1}