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JEE Main & Advanced Mathematics Differentiation Question Bank Derivative at a point Standard Differentiation

  • question_answer
    \[f(x)={{x}^{2}}-3x\], then the points at which \[f(x)=f'(x)\]are

    A)            1, 3

    B)            1, ? 3

    C)            ? 1, 3

    D)            None of these

    Correct Answer: D

    Solution :

               \[f(x)={{x}^{2}}-3x\]and \[f'(x)=2x-3\]            But \[f(x)=f'(x)\Rightarrow {{x}^{2}}-3x=2x-3\]Þ \[{{x}^{2}}-5x+3=0\]            \[\therefore x=\frac{5\pm \sqrt{25-12}}{2}=\frac{5\pm \sqrt{13}}{2}\].


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