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Question

The length of largest continuous interval in which function f(x)=4xtan2x is monotonic is

A
π/2
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B
π/4
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C
π/8
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D
π/16
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Solution

The correct option is B π/4
f(x)>0 for monotonically increasing
4tan2x+8xsec22x>0
tan2x>2xsec22x
sin2xcos2x>2x1cos22x
sin4x2>2x
Or
sin4x>4x
Or
sin4x4x>1.
Hence
4xϵ[π2,π2]
xϵ[π8.π8]
Hence length of the interval is
=π8+π8
=π4

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