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Question

If f(x)=2x+cot1x+log(1+x2x), then f(x)

A
Increases in [0,)
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B
Decreases in [0,)
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C
Neither increases nor decreases in [0,)
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D
Increases in (,)
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Solution

The correct options are
B Increases in [0,)
C Increases in (,)
f(x)=2+(11+x2)+2x21+x211+x2x=211+x2+x1+x21+x2(1+x2x)=211+x211+x2x2[0,);1+x2[1,)11+x2(0,1]111+x2[0,1)f(x)=(111+x2)+(111+x2)f(x)>0,xR
Hence f(x) increases xR

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