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Monotonically Increasing Functions

fx = sin x - ...

Question

$f (x) = sin x - a x$ is decreasing in $R$ if

a > 1

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a < 1

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a > \frac{1}{2}

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a < \frac{1}{2}

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Solution

The correct option is B $a > 1$
$f^{'} (x) < 0$
$f^{'} (x) = cos x - a < 0$
$a > cos x$
$a > [- 1, 1]$
$\Rightarrow a > 1$ .

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