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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2013

  • question_answer
        If\[h(x)={{x}^{m/n}}\]for\[x\in R,\]where\[m,n\]are odd numbers and\[0<m<n,\]then\[y=h(x)\]has

    A)  no local extremism

    B)  one local maximum

    C)  one local minimum

    D)  None of the above

    Correct Answer: A

    Solution :

                    \[h(x)=\frac{m}{n}.{{x}^{m-n/n}}=\frac{m}{n}=\frac{m}{n}.{{x}^{-1(even/odd)}}\] As,\[h(x)\]undefined at\[x=0\]and\[h(x)\]does not change its sign in the neighbor hood. So, no extremums.


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