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

  • question_answer
    If the curve \[y=a{{x}^{2}}-6x+b\] passes through (0, 2) and has its tangent parallel to the x-axis at \[x=\frac{3}{2},\] then

    A) a = b = 0

    B) a = b = 1

    C) a = b = 2

    D) a = b = -1

    Correct Answer: C

    Solution :

    [c] \[y=a{{x}^{2}}-6x+b\] passes through (0, 2). i.e., \[2=0-0+b\] or \[b=2\] Again, \[\frac{dy}{dx}=2ax-6\] At \[x=\frac{3}{2},\frac{dy}{dx}=3a-6\] Since tangent is parallel to x-axis, \[\frac{dy}{dx}=0\] or \[3a-6=0\] or \[a=2\].        Hence, \[a=2,b=2\].


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