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JEE Main & Advanced JEE Main Paper (Held On 26 May 2012)

  • question_answer
    Let \[f;\left( -\infty ,\infty  \right)\to \left( -\infty ,\infty  \right)\] be defined by \[f(x)={{x}^{3}}+1.\] Statement 1: The function f has a local extremumatx=0 Statement 2: The function f is continuous and differentiable on \[\left( -\infty ,\infty  \right)\] and f'(0)=0.   JEE Main Online Paper (Held On 26-May-2012)  

    A)  Statement 1 is true. Statement 2 is false.

    B)                        Statement 1 is true. Statement 2 is true, Statement 2 is a correct explanation for Statement 1.

    C)                         Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for Statement 1.

    D)                        Statement 1 is false, Statement 2 is true.

    Correct Answer: D

    Solution :

                    Let \[f:(-\infty ,\infty )\to (-\infty ,\infty )\]be defined by \[f(x)={{x}^{3}}+1.\] Clearly,\[f(x)\] is symmetric along y = 1 andit has neither maxima nor minima. \[\therefore \]Statement - 1 is false. Hence, option (d) is correct.


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