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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Mock Test - Application of Derivatives

  • question_answer
    The slope of the tangent to the curve \[y=\sqrt{4-{{x}^{2}}}\] at the point where the ordinate and abscissa equal is

    A) -1

    B) 1

    C) 0                     

    D) none of these

    Correct Answer: A

    Solution :

    [a] Here, y>0. Putting \[y=x\] in \[y=\sqrt{4-x}\], we get\[x=\sqrt{2},-\sqrt{2.}\] So, the point is\[(\sqrt{2},\sqrt{2})\]. Differentiating \[{{y}^{2}}+{{x}^{2}}=4\]w.r.t. x, we get \[2y\frac{dy}{dx}+2x=0\] Or \[\frac{dy}{dx}=-\frac{x}{y}\] \[\therefore At(\sqrt{2},\sqrt{2}),\frac{dy}{dx}=-1\]


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