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 Bπ/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