A) \[a<1\]
B) \[a\ge 1\]
C) \[a\ge \sqrt{2}\]
D) \[a<\sqrt{2}\]
Correct Answer: B
Solution :
Since \[f(x)=\sqrt{3}\sin x-\cos x-2ax+b\] is decreasing for all real values of \[x,\]therefore \[f'(x)<0\]for all x. Þ \[\sqrt{3}\cos x+\sin x-2a<0\]for all x \[\Rightarrow \frac{\sqrt{3}}{2}\cos x+\frac{1}{2}\sin x<a\]for all x Þ \[\sin \left( x+\frac{\pi }{3} \right)<a\]for all x Þ\[a\ge 1,\,\left[ \because \sin \left( x+\frac{\pi }{3} \right)\le 1 \right]\].You need to login to perform this action.
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