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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    The values of x, at which the first derivative of the function \[{{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{2}}\]w.r.t. x is \[\frac{3}{4}\], are [MP PET 1998]

    A)                    \[\pm \,2\]

    B)            \[\pm \frac{1}{2}\]

    C)                    \[\pm \frac{\sqrt{3}}{2}\]

    D)  \[\pm \frac{2}{\sqrt{3}}\]

    Correct Answer: A

    Solution :

               Given \[f(x)={{\left( \sqrt{x}+\frac{1}{\sqrt{x}} \right)}^{2}}\]                    \[f(x)=x+\frac{1}{x}+2\] and \[f'(x)=3/4\]                    So, \[1-\frac{1}{{{x}^{2}}}=\frac{3}{4}\] Þ \[\frac{1}{{{x}^{2}}}=\frac{1}{4}\] Þ \[x=+2,\,-2\].


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