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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Mock Test - Application of Derivatives

  • question_answer
    Let \[f\,\left( 1 \right)=-\,2\] and \[f'(x)\ge 4.2\] for \[1\le x\le 6\]. The smallest possible value of f(6) is

    A) 9                     

    B) 12

    C) 15                    

    D) 19

    Correct Answer: D

    Solution :

    [d] Using Lagrange's mean value theorem, for some \[c\in (1,6)\] \[f'(c)=\frac{f(6)-f(1)}{5}=\frac{f(6)+2}{5}\ge 4.2\] Or \[f(6)+2\ge 21\] Or \[f(6)\ge 19\]


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