A) \[a\ge \sqrt{2}\]
B) \[a<\sqrt{2}\]
C) \[a\ge 1\]
D) \[a<1\]
Correct Answer: A
Solution :
We have; \[f(x)=\sin x-\cos x-ax+b\] \[\Rightarrow \,\,f'(x)=\cos x+\sin x-a\] \[\Rightarrow \,f'(x)<0\,\,\forall \,\,x\in R\] \[\Rightarrow \,(\cos x+\sin x)<a\,\,\forall \,\,x\in R\] As the max. value of \[(\cos x+\sin x)\]is \[\sqrt{2}\] The above is possible when \[a\ge \sqrt{2}\]You need to login to perform this action.
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