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J & K CET Engineering J and K - CET Engineering Solved Paper-2010

  • question_answer
    For the function \[f(x)=|x-8|,\,0\le x\le 16,\] the Rollers theorem is not applicable as

    A)  the function is not continuous at\[x=8\]

    B)  \[f(0)\ne f(16)\]

    C)  the function is not differentiable at \[x=8\]

    D)  the function is not differentiable at all points in \[(0,\,16)\]

    Correct Answer: C

    Solution :

    Given, function \[f(x)=|x-8|,\,0\le x\le 16\] This function is continuous at \[x=8,\] since \[LHL=RHL=f(8)\] Also, \[f(0)=f(16)=8\] But, this function is not differentiable at \[x=8.\] Hence, for the given function Rolle?s theorem is not applicable, since the function is not differentiable at \[x=8.\]


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