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Question

The function f(x)=sinxx is decreasing in the interval

A
(π2,0)
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B
(0,π2)
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C
(π4,0)
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D
None of these
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Solution

The correct option is A (0,π2)
f(x)=sinxx
Let f(x)=xcosxsinxx2
Let g(x)=xcosxsinx
=cosx(xtanx)
where cosx>0
xtanx<0
g(x)<0
f(x)<0
f(n) is a decreasing function in (0,π2)

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