JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Increasing and Decreasing Function

  • question_answer
    The function \[x+\frac{1}{x},(x\ne 0)\]is a non-increasing function in the interval

    A)            [? 1, 1]

    B)            [0, 1]

    C)            [?1, 0]

    D)            [?1,2]

    Correct Answer: A

    Solution :

               Let \[f(x)=y=x+\frac{1}{x}\]            Differentiating with respect to x, we get            \[\frac{dy}{dx}=f'(x)=1-\frac{1}{{{x}^{2}}}\le 0\]\[\,\Rightarrow 1\le \frac{1}{{{x}^{2}}}\] or \[{{x}^{2}}\le 1\]            Hence \[x\in [-1,\,1]\].


You need to login to perform this action.
You will be redirected in 3 sec spinner