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If the function $⨍ (x)=cos |x| -2ax+b$ increases along the entire number scale, then the range of values of a is

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$a = \frac{1}{2}$

$a < - \frac{1}{2}$

$a > - \frac{1}{2}$

$a > \frac{1}{2}$

answer is B.

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Detailed Solution

$⨍ (x)=cos x-2ax+b ⨍^{1} (x)=-sin x-2a$

$⨍ (x)$ is incresing

$\Rightarrow ⨍^{1} (x)>0 - \sin x - 2 a > 0 2 a < - \sin x 2 a < - 1 a < \frac{- 1}{2}$

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