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Q.

The function  fx=4x3−3x26−2sinx+2x−1cosx

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a

Increasing in 12,∞

b

Decreases in −∞,1

c

Increasing in −∞,12

d

Decreases in 12,∞

answer is A.

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Detailed Solution

f'x=2x−1x−sinx⇒⇒f'x≥0 inx∈12,∞andf'x≤0 in x∈∞,12
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The function  fx=4x3−3x26−2sinx+2x−1cosx