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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 33

  • question_answer
    If \[\operatorname{f}(x) = a\left| sin x \right|\,+\,\,b{{e}^{\left| x \right|}}\,+c{{\left| x \right|}^{3}}\] and if is differentiable at \[\operatorname{x}= 0\], then

    A) \[a=b=c=0\]    

    B) \[a=0,\,\,b=0,\,\,c\in R\]

    C) \[b=c=0,\,\,a\in R\]       

    D) \[c=0,a=0,\,\,b\in R\]

    Correct Answer: A

    Solution :

    Given \[\operatorname{f}(x)=\,\,a\left| sin\,x \right|\,+\,b{{e}^{\left| x \right|}}\,+\,\,c{{\left| x \right|}^{3}}\] Since, \[\left| x \right|\] is non-differentiable at \[\operatorname{x} =0\] \[\therefore \,\,\,f(x)\] cannot be differentiable at \[x= 0\] Hence, \[\operatorname{a}=b= c = 0.\]


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