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BCECE Engineering BCECE Engineering Solved Paper-2002

  • question_answer
    The value of a for which the function \[f(x)=a\sin x+\frac{1}{3}\sin 3x\] has an extremum at   \[x=\frac{\pi }{3},\] is:

    A)  1                            

    B)        \[-1\]                    

    C)  0                            

    D)  2

    Correct Answer: D

    Solution :

    Key Idea: The extremum point of a function in which \[f(x)=0.\] We have                 \[f(x)=a\sin x+\frac{1}{3}\sin 3x\]                 \[\Rightarrow \]               \[f(x)=a\cos x+\cos 3x\] Since, it is given that at \[x=\frac{\pi }{3},f(x)\]is extremum. i.e.,               \[f\left( \frac{\pi }{3} \right)=0\] \[\Rightarrow \]\[a\cos \left( \frac{\pi }{3} \right)+\cos 3\left( \frac{\pi }{3} \right)=0\] \[\Rightarrow \]               \[a\left( \frac{1}{2} \right)+(-1)=0\] \[\Rightarrow \]               \[a=2\]


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