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

  • question_answer
    What is the slope of the tangent to the curve\[x={{t}^{2}}+3t-8,y=2{{t}^{2}}-2t-5\,\,at\,\,t=2\]?

    A) 7/6

    B) 6/7

    C) 1

    D) 5/6

    Correct Answer: B

    Solution :

    [b] \[\frac{dx}{dt}=2t+3,\frac{dy}{dt}=4t-2\] \[\frac{dy}{dx}=\frac{dy/dt}{dx/dt}=\frac{4t-2}{2t+3}\] slope at \[t=2=\frac{dy}{dx}/t=2=\frac{4(2)-2}{2(2)+3}=\frac{6}{7}\]


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