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JEE Main & Advanced JEE Main Paper Phase-I Held on 07-1-2020 Morning

  • question_answer
    Let the function, \[f:[-7,\text{ }0]\to R\] be continuous on \[[-7,\text{ }0]\] and differentiable on \[(-7,\text{ }0)\]. If \[f(-7)=-3\] and \[f'(x)\le 2\], for all \[x\in (-7,0)\] then for all such functions \[f,\text{ }f(-1)+f(0)\] lies in the interval [JEE MAIN Held on 07-01-2020 Morning]

    A) \[[-3,\,\,11]\]      

    B) \[(-\infty ,\,\,20]\]

    C) \[(-\infty ,\,\,11]\]

    D) \[[-6,\,\,20]\]

    Correct Answer: B

    Solution :

    [b]
    Apply LMVT in \[[-7,\,\,-1]\]
    \[\frac{f(-1)-f(-7)}{6}\le 2\]
    \[\Rightarrow f(-1)+3\le 12\]
    \[f(-1)\le 9\]
    Now apply LMVT in \[[-7,0]\]
    \[\frac{f(0)-f(7)}{7}\le 2\]
    \[f(0)\le 11\]
    Hence \[f(-1)+f(0)\le 20\]


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