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JEE Main & Advanced Sample Paper JEE Main Sample Paper-33

  • question_answer
    Let \[f(x)=\left\{ _{a{{x}^{2}}+bx+c\,\,\,\,\,\,\,\,\,\,\,\,x>1}^{{{x}^{3}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x\le 1} \right.\,\] If \[f''\left( x \right)\]is continuous everywhere, then which one of the following is correct?

    A)  \[a=3,b=-3,c=1\]

    B)  \[a=-3,b=3,c=1\]

    C)  \[a=3,b=3,c=-2\]

    D)  cannot be determined

    Correct Answer: A

    Solution :

    Continuity of \[f\left( x \right)\text{ }at\text{ }x\text{ }=\text{ }1~\]             \[\Rightarrow \,\,a+b+c=1\] Continuity of \[f'\left( x \right)\text{ }at\text{ }x\text{ }=\text{ }1\]             \[\Rightarrow \,3=2a+b\] Continuity of \[f'\left( x \right)\text{ }at\text{ }x\text{ }=\text{ }1\] \[\Rightarrow \,6=2a\,\Rightarrow \,a=3\] Hence, \[b=-3\text{ }and\text{ }c=1\]


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