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

  • question_answer
    For the every value of x the function \[f(x)=\frac{1}{{{5}^{x}}}\]is 

    A)            Decreasing           

    B)            Increasing

    C)            Neither increasing nor decreasing

    D)            Increasing for x > 0 and decreasing for x < 0

    Correct Answer: A

    Solution :

               \[f(x)={{5}^{-x}}\]                    Þ\[f'(x)=-{{5}^{-x}}{{\log }_{e}}5=-\frac{{{\log }_{e}}5}{{{5}^{x}}}\] Þ \[f'(x)<0\] for all \[x\]                    i.e., \[f(x)\] is decreasing for all \[x.\]


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