JEE Main & Advanced AIEEE Solved Paper-2002

  • question_answer
    The function \[f(x)={{\cot }^{-1}}x+x\] increases in the interval   AIEEE  Solved  Paper-2002

    A) \[(1,\infty )\]   

    B)                           \[(-1,\infty )\]      

    C)           \[(-\infty ,\infty )\]        

    D) \[(0,\infty )\]

    Correct Answer: C

    Solution :

                      A function f(x) is said to be increasing function, if \[f'(x)\ge 0\]. Since,       \[f(x)={{\cot }^{-1}}x+1\] On differentiating w.r.t. x, we get \[f'(x)=-\frac{1}{1+{{x}^{2}}}+1=\frac{{{x}^{2}}}{1+{{x}^{2}}}\] Hence, \[f'(x)\] increasing function since \[f'(x)\ge 0\]for all \[x\].

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