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JEE Main & Advanced Mathematics Applications of Derivatives Question Bank Critical Thinking

  • question_answer
    If the normal to the curve \[y=f(x)\] at the point \[(3,\,4)\] makes an angle \[\frac{3\pi }{4}\]with the positive x-axis then \[f'(3)\] is equal to [IIT Screening 2000; DCE 2001]

    A) \[-1\]

    B) \[-\frac{3}{4}\]

    C) \[\frac{4}{3}\]

    D) \[1\]

    Correct Answer: D

    Solution :

    • Slope of the normal = \[\frac{-1}{dy/dx}\]           
    • Þ  \[\tan \frac{3\pi }{4}=\frac{-1}{{{\left( dy/dx \right)}_{(3,\,4)}}}\]           
    • \ \[{{\left( \frac{dy}{dx} \right)}_{(3,\,4)}}=1\],   \ \[{f}'(3)=1.\]


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