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JEE Main & Advanced Sample Paper JEE Main Sample Paper-29

  • question_answer
    Let\[\left\{ \begin{matrix}    -{{x}^{3}}+{{\log }_{2}}b, & 0\le x<1  \\    3x, & 1\le x\le 3  \\ \end{matrix} \right.\] . The set of real values of b for which \[f(x)\] has smallest value at \[x=1\], is

    A) \[\left( 0,8 \right]\]                                        

    B) \[\left[ 8,\infty  \right)\]

    C) \[\left[ 16,\infty  \right)\]                            

    D) \[\left( 0,16 \right]\]

    Correct Answer: C

    Solution :

    If the function \[f(x)\] has smallest value at\[x=1\], then \[\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,f(x)\ge f(1)\Rightarrow -1+{{\log }_{2}}b\ge 3\]      \[\Rightarrow {{\log }_{2}}b\ge 4\Rightarrow b\ge 16\] \[\therefore b\in [16,\,\,\infty )\]


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