2. Sample Papers
  3. JEE Main & Advanced

JEE Main & Advanced Sample Paper JEE Main Sample Paper-1

  • question_answer
    The value 6f a for which the function  f(x) = sin x - cos x - ax + b decreases for \[x\in R\]is given by                        

    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.
You will be redirected in 3 sec spinner