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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    If the mean value theorem is\[f(b)-f(a)=(b-a)f'(c)\]. Then, for the function \[{{x}^{2}}-2x+3\] in \[\left[ 1,\frac{3}{2} \right]\] the value of c is

    A) 6/5

    B) 5/4

    C) 4/3

    D) 7/6

    Correct Answer: B

    Solution :

    [b] Let \[f(x)={{x}^{2}}-2x+3\] Since, \[f'(c)=\frac{f\left( \frac{3}{2} \right)-f(1)}{\frac{3}{2}-1}\]  (given) \[\Rightarrow 2c-2=\frac{\frac{9}{4}-\frac{6}{2}+3-(1-2+3)}{\frac{3}{2}-1}\Rightarrow c=\frac{5}{4}\]


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