A) \[a\ge \sqrt{2}\]
B) \[a\ge 1\]
C) \[a<\sqrt{2}\]
D) \[a<1\]
Correct Answer: A
Solution :
Since, \[f(x)=\sin x-\cos x-ax+b\] \[\therefore \]\[f'(x)=\cos x+\sin x-a\] Thus, the function decreases, if \[\cos x+\sin x-a\le 0\] \[\Rightarrow \]\[\cos x+\sin x\le a\] \[\Rightarrow \]\[\sqrt{2}\sin \left( x+\frac{\pi }{4} \right)\le a\]\[\Rightarrow \]\[\sqrt{2}\le a\] \[\therefore \]The function decreases only, if \[a\ge \sqrt{2}\].You need to login to perform this action.
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