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

  • question_answer
    If f(x) and g(x) are differentiable functions for \[0\le x\le 1\] such that f(0)=10, g(0)=2,  f(1)=2, g(1)=4, then in the interval (0, 1),

    A) f'(x) =0 for all x

    B) f'(x)+4g'(x)=0 for at least one x

    C) f'(x)=2g'(x) for at most done x

    D) none of these

    Correct Answer: B

    Solution :

    [b] We know that there exists at least one x in (0, 1) for which \[\frac{f(1)-f(0)}{g(1)-g(0)}=\frac{f'(x)}{g'(x)}\] Or \[\frac{2-10}{4-2}=\frac{f'(x)}{g'(x)}\]or \[f'(x)+4g'(x)=0\] For at least one x in (0, 1).


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