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  4. What is the value of b for which f(x)= sin x-bx+c is decreasing in the interval (-∞ ,∞ ) ?

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Q. What is the value of b for which $ f(x)=\sin x-bx+c $ is decreasing in the interval $ (-\infty ,\infty ) $ ?

JamiaJamia 2011

Solution:

Given, $ f(x)=\sin x-bx+c $ $ \Rightarrow $ $ f(x)=\cos x-b $ Since, it is decreasing, $ \therefore $ $ f(x)<0 $ $ \Rightarrow $ $ \cos x1 $ $ (\because \cos x\le 1) $