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Q.

The interval on which the function sin2x–x, 0<x<π2
decreases is

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a

π6,π2

b

0,π2

c

0,π6

d

0,π4

answer is D.

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Detailed Solution

fx=sin 2x-x f'x=cos 2x2-1

fx is decreases

f'x<0 2cos2x-1<0 cos 2x<1/2 2x>π3 x>π6 xπ6, π2 Becasue given x0, π2

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The interval on which the function sin2x–x, 0<x<π2decreases is