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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Self Evaluation Test - Application of Derivatives

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

    A) 0

    B) 1

    C) -1

    D) 2

    Correct Answer: D

    Solution :

    [d] Let \[f(x)=p\,\,\sin x+\frac{\sin 3x}{3}\] Differentiate both side w.r.t(x). \[\Rightarrow f'(x)=p\,\,\cos \,\,x+\frac{3\cos 3x}{3}=p\cos x+\cos 3x\] It is given that \[f(x)\] has extreme value at \[x=\pi /3\] \[\therefore f'\left( \frac{\pi }{3} \right)=0\Rightarrow p\cos \frac{\pi }{3}+\cos \pi =0\] \[\Rightarrow \frac{p}{2}-1=0\Rightarrow p=2\]


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