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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 43

  • question_answer
    Let \[f(x)={{x}^{3}}+5x+8\] and \[x=\alpha \] be a point such that \[f'(\alpha )\ne \frac{f(b)-f(a)}{b-a}\] for any values of \[a,b,\in R\]. Then the number of such points is

    A) \[0\]                      

    B)        \[1\]           

    C) \[2\]                     

    D)        More than 2

    Correct Answer: B

    Solution :

    [b] According to given information, a is the point of inflection of \[y=f(x)\]. \[\therefore \,\,\,\,\,\,f''(\alpha )=0\Rightarrow \alpha =0\] \[f'(0)=5\] and  \[\frac{f(b)-f(a)}{b-a}={{b}^{2}}+ab+{{a}^{2}}+5\] \[=\left( b+\frac{a}{2} \right)+\frac{3{{a}^{2}}}{4}+5>5\,\,\forall a\ne b\in R\]         


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