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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    If f is a real- valued differentiable function satisfying                                                                           \[|f(x)-f(y)|\le {{(x-y)}^{2}},x,y\in R\]  and                                                                                                 \[f(0)=0\] , then                                                                                                   \[f(1)\]  equal          [AIEEE 2005]

    A)            2

    B)            1

    C)            ?1

    D)            0

    Correct Answer: D

    Solution :

    \[\underset{x\to y}{\mathop{\lim }}\,\left| \frac{f(x)-f(y)}{x-y} \right|\le \underset{x\to y}{\mathop{\lim }}\,|x-y|or|f'(x)|\le 0\]                                                                                            \[\Rightarrow f'(x)=0\Rightarrow f(x)\] is constant, As                                                                                                 \[f(0)=0\]                    \                                                                                                 \[f(1)=0\] .


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