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CEE Kerala Engineering CEE Kerala Engineering Solved Paper-2000

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

    A)  1                            

    B)         \[-1\]                   

    C)  2                            

    D)         0

    E)  \[-2\]

    Correct Answer: C

    Solution :

    \[f(x)=a\sin x+\frac{1}{3}\sin 3x\] \[f(x)=a\cos x+\frac{3}{3}\cos 3x=0,\]at\[x=\frac{\pi }{3}\] \[\Rightarrow \]               \[a\cos \frac{\pi }{3}+\cos \frac{\pi }{3}.3=0\] \[\Rightarrow \]               \[a.\frac{1}{2}+(-1)=0\] \[\Rightarrow \]               \[a=2\]


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