JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Maxima and Minima

  • question_answer
    The least value of the sum of any positive real number and its reciprocal is                                            [MP PET 1994]

    A)            1

    B)            2

    C)            3

    D)            4

    Correct Answer: B

    Solution :

               \[f(x)=x+\frac{1}{x}\Rightarrow f'(x)=1-\frac{1}{{{x}^{2}}}\]            Þ \[f'(x)=0\Rightarrow {{x}^{2}}-1=0\Rightarrow x=1,-1\]            But given that x is positive, hence at \[x=1,\,\,f(x)=1+\frac{1}{1}=2\].


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