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

  • question_answer
    How many tangents are parallel to x-axis for the curve\[y={{x}^{2}}-4x+3\]?

    A) 1

    B) 2

    C) 3

    D) No tangent is parallel to x-axis

    Correct Answer: A

    Solution :

    [a] Let \[y={{x}^{2}}-4x+3\] Differentiate both sides w.r.t. ?x? \[\frac{dy}{dx}=2x-3\] So, slope \[=2x-3\] Since, tangent is \[\parallel \] to x = axis \[\therefore \] slope = 0 \[\Rightarrow \frac{dy}{dx}=0\Rightarrow 2x-3=0\Rightarrow x=\frac{3}{2}\] \[\Rightarrow \] one tangent


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