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JEE Main & Advanced Sample Paper JEE Main Sample Paper-15

  • question_answer
    Let \[f:R\to R,\]\[f(x)=2{{x}^{3}}-3(k+2){{x}^{2}}+12kx-7,\] \[-4\le k\le 6,k\in I,\], then the value of k for which f(x) is invertible is

    A)  0                                            

    B)  1

    C)  2                                            

    D)  3

    Correct Answer: C

    Solution :

    \[f(x)=2{{x}^{3}}-3(k+2){{x}^{2}}+12kx-7,\] \[-4\le k\le 6,k\in I\] \[f'(x)=6({{x}^{2}}-(k+2)x+2k)\] \[f'(x)=6(x-k)(x-2)\] for \[f(x)\] to be invertible, ?k? must be ?2? only. Ans.


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