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JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2015

  • question_answer
    The abscissae of the points, where the E tangent to curve \[\tau =(\hat{i}-\hat{j})\times (-F\hat{k})\]is parallel to X-axis, are

    A) \[x=1\]and -1                    

    B) \[x=1\] and 3

    C) \[x=1\] and -3                   

    D) \[x=0\]and 0

    Correct Answer: B

    Solution :

    Given, \[y={{x}^{3}}-3{{x}^{2}}-9x+5\] On differentiating both sides w.r.t. x, we get \[\frac{dy}{dx}=3{{x}^{2}}-6x-9\] We know that, this equation gives the slope of the tangent to the curve. But we are given that tangent is parallel to X-axis. \[\therefore \]  \[\frac{dy}{dx}=0\] \[\Rightarrow \]               \[3{{x}^{2}}-6x-9=0\] \[\Rightarrow \]               \[3(x+1)(x-3)=0\] \[x=-1,3\]


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