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J & K CET Engineering J and K - CET Engineering Solved Paper-2008

  • question_answer
    The point on the curve \[y={{x}^{3}}\]at which the tangent to the curve is parallel to the x axis, is

    A)  \[(2,2)\]          

    B)  \[(3,3)\]

    C)  \[(4,4)\]          

    D)   \[(0,0)\]

    Correct Answer: D

    Solution :

    Given curve is \[y={{x}^{3}}\] On differentiating w.r.t.x, we get \[\frac{dy}{dx}=3{{x}^{2}}\] Since, the tangent is parallel to x-axis \[\therefore \] \[\frac{dy}{dx}=0\] \[\Rightarrow \] \[3{{x}^{2}}=0\] \[\Rightarrow \] \[x=0,\,y=0\]


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