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JEE Main & Advanced Mathematics Functions Question Bank Differentiability

  • question_answer
    If  \[f(x)={{x}^{2}}-2x+4\] and \[\frac{f(5)-f(1)}{5-1}=f'(c)\] then value of  c will be [AMU 2005]

    A)            0

    B)            1

    C)            2

    D)            3

    Correct Answer: D

    Solution :

               \[f(x)={{x}^{2}}-2x+4\]; \[f'(x)=2x-2\]                    At \[x=c\], \[f'(c)=2c-2\]                    \[f(5)={{5}^{2}}-2(5)+4=19\]; \[f(1)={{1}^{2}}-2(1)+4=3\]                    \[\frac{f(5)-f(1)}{5-1}=f(c)\] Þ \[\frac{19-3}{5-1}=2c-2\] Þ \[\frac{16}{4}=2c-2\]                    Þ \[4=2c-2\] Þ \[2c=6\] or \[c=3\].


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