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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2004

  • question_answer
    If\[f(x)=\left\{ \begin{matrix}    x+1 & when\,x<2  \\    2x-1, & when\,x\ge 2  \\ \end{matrix} \right.,\]then at\[a=2,f'(x)\]is equal to

    A)  10              

    B)  1

    C)  2                 

    D)  does not exist

    Correct Answer: D

    Solution :

     \[f(x)=\left\{ \begin{matrix}    x+1 & when & x<2  \\    2x-1, & when & x\ge 2  \\ \end{matrix} \right.\] When \[x<2,\] \[f(x)=x+1\] \[\Rightarrow \] \[f'(x)=1\] and when\[x\ge 2,f(x)=2x-1\] \[\Rightarrow \] \[f'(x)=2\] Hence, at\[x=2,f'(x)\]does not exist.


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