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CET Karnataka Engineering CET - Karnataka Engineering Solved Paper-2009

  • question_answer
    If \[f(x)=\frac{g(x)+g(-x)}{2}+\frac{2}{{{[h(x)+h(-x)]}^{-1}}}\]where g and h are differentiable function, then \[f'(0)\]

    A)  \[1\]                                    

    B)  \[\frac{1}{2}\]

    C)  \[\frac{3}{2}\]                                  

    D)  \[0\]

    Correct Answer: D

    Solution :

    Given., \[f(x)=\frac{g(x)+g(-x)}{2}+\frac{2}{{{[h(x)+h(-x)]}^{-1}}}\] \[\Rightarrow \] \[f(x)=\frac{g(x)+g(-x)}{2}+2[h(x)+h(-x)]\] On differentiating w.r.t.x, we get \[f'(x)=\frac{g'(x)-g'(-x)}{2}+2[h'(x)-h'(-x)]\] \[\therefore \] \[f'(0)=\frac{g'(0)-g'(0)}{2}+2[h'(0)-h'(0)]\]                 \[=0\]


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