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JEE Main & Advanced AIEEE Solved Paper-2010

  • question_answer
      Let\[f:(1,1)\to R\]be a differentiable function with\[f(0)=1\]and\[f'(0)=1.\]Let\[~g(x)=\] \[=[f{{(2f(x)+2]}^{2}}\]Then\[g'(0)=\]       AIEEE  Solved  Paper-2010

    A) 4

    B) -4                         

    C) 0                             

    D) -2  

    Correct Answer: B

    Solution :

    \[g'(x)=2[f(2f(x)+2)].f'(2f(x)+2).2f'(x)\]\[g'(0)=2[f(2.f(0)+2)].f'(2f(0)+2).2f'(0)\] \[=2[f(0)].f'(0).2\] \[=2(-1).(1).2\] \[=\text{ }4\]


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