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Find the value of a in order that f(x)=s...

Find the value of `a` in order that `f(x)=sqrt(3)sinx-cosx-2a x+b` decreases for all real values of `xdot`

Text Solution

Verified by Experts

The correct Answer is:
`[1,oo]`
Since f(x) `=sqrt(3) sin x =cos x -2ax +b` is decreasing forall real vallues of `x , f'(x) le 0` for all x
or `sqrt(3) cos x +sin 4 x -2a le 0 forall x`
or `(sqrt(3)/(2)cos x+ (1)/(2)) sin 4xle a forall x`
or `age1[(therefore sin x+(pi)/(3)le1)]`
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